Transcript for:
Notes on Simplifying Algebraic Expressions

[Music] welcome to math with Mr J in this video I'm going to cover how to simplify algebraic expressions I'll cover how to combine like terms and how to use the distributive property in order to do so we will start with an introduction to combining like terms then we will take a look at more examples after that we will take a look at an introduction to the distributive property following that introduction we will take a look look at more examples and then lastly we will simplify expressions by using both combining like terms and the distributive property now remember like terms are terms with the same variables to the same Powers when we combine like terms we look for any like terms in the given algebraic expression and combine them into one term by combining like terms we can simplify expressions that just means we can rewrite the original expression in a simpler and easier way to understand and work with let's jump into number one where we have 9x + 3x we will start with this basic expression and work our way up so we have two terms in this expression 9x and 3X both terms have the same variable of X and these variables of X are to the same power remember when we don't have an exponent attached to a variable there is an understood exponent of one anything to the power of one is just itself so 9x and 3X are like terms now when we combine like terms all we need to do is add or subtract the coefficients the numbers in front of the variables the coefficients in number one are 9 and 3 we have a positive 9x plus a positive 3 X so let's add those coefficients 9 + 3 is 12 and then we have the variable of X and that's it we took those two like terms 9x and 3X and combined them into one term 12x 12x is equivalent to 9x + 3x so we didn't change the value of the expression so 12x is our final simplified expression let's move on to number two where we have a 8 G + 7 + 5 G + 2 are there any like terms that we can combine in order to simplify this expression yes we have 8G and 5G both of those terms have that variable of G and then we have constant terms 7 and 2 I'll box in the constant terms to separate them from The 8G and the 5G G now we can combine like terms we have 8 G + 5G that gives us 13 G and then we have 7 + 2 that gives us 9 so we end up with 13 G + 9 and that's our simplified expression that expression of 13 G + 9 is equivalent to the original expression we were just able to simplify the original expression by combining like terms we started with four total terms but we were able to combine like terms and now we only have two total terms let's move on to number three where we have 6 y^2 + 10 y + 2 y 2 + 3 y + y let's find any like terms that we can combine we'll start with 6 y^2 2 y^2 is a like term both of those terms have that variable of Y to the power of 2 now do we have any other like terms within this algebraic expression that we can combine yes 10 Y and I will box these terms in in order to separate them from the y^2 terms 3 Y and then y now I do want to mention this term right here the Y the variable by itself the coefficient is one we took don't have a coefficient written in front whenever you see that the coefficient is one there is an understood one in front of a variable and it can be helpful to write that one in there when you combine like terms so you can always write that one if you would like now since this algebraic expression has five terms and we are working our way up to more complicated algebraic expressions we're going to use a Strate y to help us organize the expression before we combine like terms we are going to rearrange and rewrite the expression and put the like terms next to each other I'll start with 6 y^ 2ar plus the like term of 2 y^ 2 plus now we have the Y terms so 10 y + 3 y + one y so now all of the like terms are next to each other and it's a little easier to see what we can combine so this is a strategy to keep in mind now do you have to do this step in order to combine like terms no but it can be helpful now we can combine like terms we will start with 6 y^2 + 2 y^2 so add the coefficients 6 + 2 is is 8 and then we have y^2 plus now we can combine the Y terms so we have 10 + 3 + 1 10 + 3 is 13 + 1 is 14 so we get 8 y^2 + 14 Y and that's the simplified expression we now have an equivalent expression that is simpler than the original we simplified the expression we went from five terms to two terms let's move on to number four where we have 7x + 2 y - 4x + 2 y let's find any like terms that we can combine we will start with 7x and -4x now when we combine like terms a term is going to take the sign that's in front of it so this is -4x then we have 2 Y and 2 y so let's box those terms in in order to separate them from the X terms now we can rewrite this expression with the like terms next to each other we will start with 7x minus 4X so we have a -4x there make sure to bring the sign that's in front of the term with it when we rewrite the expression Plus plus 2 y so now we have the Y terms plus another 2 y now we can combine like terms so we have 7X - 4x or you can think of this as 7x being combined with -4x however you want to think about it 7 - 4 is 3 and then we have the x or if you're thinking about it as 7x combined with -4x 7 and -4 give us 3 as well then we have our 2 y + 2 y that gives us+ 4 y so we end up with 3x + 4 Y and that's our simplified expression we went from four total terms to two total terms by combining like terms 3x + 4 Y is equivalent to the original expression we were just able to again simplify this expression by combining like terms now I also want to go through simplifying this expression a slightly different way to start off and that's by rewriting the original expression with only addition separating the terms we do this by changing any subtraction to adding the opposite the benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms especially any negative terms it kind of organizes the expression and helps any negatives stand out I'll rewrite the expression off to the side here so 7x + 2 y - 4x + 2 y so let's rewrite subtraction as adding the opposite so adding the opposite of a positive 4 X is a 4X so adding the opposite let's rewrite the expression with that change so we have 7x + 2 y + -4x + 2 y let's rewrite that expression with like terms next to each other so 7 x + -4x + 2 y + 2 y now we can combine like terms we have 7x + -4x that gives us 3x and then we have 2 y + 2 y so that gives us plus 4 y 3x + 4 y that way as well so that's just another strategy to be aware of so there's an introduction to combining like terms let's take a look at more examples here are more examples of algebraic expressions that we will simplify by combining like terms let's jump into number one where we have 9 C + 6 D + 5D + 8 C + 2D the first thing that we need to do is identify any like terms that we can combine so are there any like terms that we can combine in this expression yes let's start with 9 C and 8 C both of those terms have the same variable to the same power both terms have the same variable of C to the same understood power of one so they are like terms remember when we don't have an exponent attached to a variable there is an understood exponent of one something is to the power of one anything to the power of one is just itself do we have any other like terms that we can combine yes we have 6D 5D and 2D all of those terms have the same variable of D to the same understood power of one so let's box those terms in in order to separate them from the other terms are there any other like terms that we can combine no all of the like terms have been identified so what we can do now we can rewrite this expression with the like terms next to each other by rewriting this expression with all of the like terms next to each other this will help us organize the expression it will make combining like terms a little simpler we have 9 C plus 8 C+ 6 D + 5 d plus 2D so now all of the like terms are next to each other and it's a little easier to see what we need to combine so this is a strategy to keep in mind now do we have to do this step in order to combine like terms no but it can be helpful now we can combine like terms let's start with 9 C and 8 C so we have 9 C + 8 C we need to add the coefficients the numbers and front of the variables so we have 9 + 8 which is 17 so we have 17 C plus and now we can combine these terms so we have 6D + 5D + 2D 6 + 5 is 11 + 2 is 13 so we have 13d and this is our final simplified expression expression 17 C + 13d now 17 C + 13d is equivalent to the original expression we went from five total terms in the original expression and simplified it to two total terms by combining like terms let's move on to number two where we have -10 a + 2 a b + 9 a + a b + 9 a - 8 let's start by identifying any like terms that we can combine so do we have any like terms that we can combine yes we have -10 a and 9 a and another 9A all three of those terms have the same variable to the same power the variable of a to the understood Power of One do we have any other like terms that we can combine yes we have two AB let's box these in in order to separate them and then AB now this term right here AB does not have a coefficient written in front whenever we see this there is an understood coefficient of one so this is 1 a and we're able to write that one in as the coefficient and it's helpful to do so when combining like terms that way you know you need to combine that one one are there any other like terms within this expression that we can combine no but we do have one more term 8 so we have a constant term of 8 and I'll Circle that term in order to separate it even though we don't have anything to combine it with we still need to include it in the simplified expression and that is -8 remember a term will take the sign that's in front of it so we have8 and - 10 a within this expression now we can rewrite this expression with the like terms next to each other we have -10 a + 9 a + 9 a plus 2 a + 1 a minus 8 now we can combine like terms let's start with with -10 a + 9 a + 9 a -10 + 9 is -1 + 9 is 8 a positive 8 so we have 8 a and then plus 2ab + 1 a 2 + 1 is 3 so we have 3 a and then lastly we have a -8 or minus 8 here so 8 a + 3 a b - 8 is our final simplified expression we went from six total terms in the original expression to three total terms in the simplified expression by combining like terms let's move on to numbers three and four where we actually have the same exact expression 4x^2 - 7 + 3x - 2x 2 + 3 we're going to go through this two slightly different ways first we will go through simplifying the expression as it currently is and that's for number three for number four we're going to rewrite the expression so all of the terms are separated only by addition we will talk more about that strategy once we get to number four let's start number three by identifying any like terms so do we have any like terms that we can combine yes we have 4x^2 and - 2x^2 both of these terms have the same variable of x to the same power of two so 4x^2 and - 2x^2 remember a term takes the sign that's in front of it so that's - 2x^2 do we have any other like terms that we can combine yes we have two constant terms -7 and three I'll box those terms in in order to separate them and then lastly we have 3x we don't have any like terms to combine 3x with but I will Circle it in order to separate it from the other terms now we can rewrite this expression with the like terms next to each other remember bring the sign that's in front of the term with it as you rewrite this expression so we have 4x^2 and then - 2x^2 is the like term so this is going to be 4x^2 - 2x^2 then we have plus 3x and then our constant terms last so we have Min - 7 a -7 plus 3 now we can combine like terms we have 4x^2 minus 2x^2 or you can think of this as combining 4x^2 and - 2x^2 however you want to think about it you'll get the same thing either way let's subtract the coefficients we have 4 Min - 2 which gives us 2 or if you thought about it as 4 combined with -2 that gives us 2 as well so this is 2 x^2 then we have + 3x and then we can combine -7 and 3 positive3 so we have -7 + 3 that gives us -4 so our final simplified expression is 2x^2 + 3x - 4 we went from five total terms in the original expression to three total terms by combining like terms let's move on to number four where we will take a look at a strategy we can use when we have subtraction or negatives involved in the expression we're going to rewrite the original expression with only addition separating the terms the benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms especially any negative terms it kind of organizes the expression and helps any negatives stand out now do you have to use this strategy no but it can be helpful so I wanted to at least go over it so let's rewrite this expression with only addition separating the terms we do this by adding the opposite so change any subtraction to adding the opposite let's change this to addition and then the opposite of positive 7 is -7 so add the opposite then let's add the opposite here as well so the opposite of positive 2x^2 is 2x^2 so let's rewrite this with those changes so we have 4x^2 plus -7 + 3x + - 2x^2 plus 3 so now all of the terms are separated only by addition now we can identify any like terms we have 4x^2 and -2 x^2 then we have -7 and 3 and then 3x now let's rewrite this expression with the like terms next to each other so we have 4x^2 plus - 2x^2 + 3x + -7 + 3 now we can combine like terms we have 4x^2 + -2 x^2 4 + -2 is 2 so we have 2 x^2 + 3x + -7 + 3 -7 + 3 is -4 so plus4 now this is correct but we can clean this up a little bit so to speak we have a double sign we are adding a negative adding a -4 adding a -4 is the same as subtracting 4 we are decreasing in value by four so we can rewrite this with just one sign we don't need both of those signs when we add a negative that's the same as just subtracting a positive so let's change this to subtracting four and again getting rid of the double sign will make this a little simpler it will clean it up we can rewrite this as 2x^2 + 3x - 4 and that's our final simplified expression so you can see that we got the same exact simplified expression for number three and four just slightly different strategies as far as organizing the expression to start now I do want to mention one last thing and it's about writing out Expressions when we write an expression we typically want any exponents first if there are multiple exponents write them from greatest to least if we have the same exponent go in ABC order and then constant terms always come last so for example in number one we have the variables of c and d both are to the understood power of one so we go in ABC order for number two we have a and ab everything here is to the understood power of one so we go in ABC order a comes first then a b and then the constant term comes last for numbers 3 and four we have X2 so the greatest exponent 2 then we have the variable of x to the understood power of one and then lastly we have the constant term so something to keep in mind when you are writing Expressions so there's how to combine like terms let's move on to the distributive property here is an introduction to the distributive property now the distributive property can help us remove parentheses within algebraic expressions this helps us simplify expressions when we do not have like terms within parentheses that we can combine now remember when we have something next to parentheses that means multiplication so we can use the distributive property to distribute whatever is on the outside of the parentheses to the terms inside the parentheses the distributive property works when we have addition or subtraction inside of the parentheses so at the top of the screen there is a general overview of the distributive property where a is being distributed to the terms inside of the parentheses the distributive property and that overview will make a lot more sense as we go through our examples let's jump into number one where we have two and then in parentheses 5 + three and we're going to do this two different ways by using the order of operations so doing what's in the parentheses first and then also using the distributive property now for number one we don't have any variables involved we are actually able to add what's in the parenthesis first and then go from there we don't have to use the distributive property but the point of number one is to show us that we get the same thing either way this is going to show us that the distributive property doesn't change the value of an expression we are able to use this strategy so again we get the same thing either way let's start by using the order of operations and doing what's in the parentheses first we have 5 + 3 which is 8 bring down the two and now we have 2 * 8 which is 16 now let's Use the distributive property and see if we still get 16 so we need to take that two on the outside of the parentheses and distribute it to the five and to the three so we have 2 * 5 + 2 * 3 2 * 5 gives us 10 + 2 * 3 gives us 6 10 + 6 is 16 so we get 16 that way as well so we can see that the distributive property doesn't change the value of an expression and we are able to use it let's move on to number two where we will apply this to an algebraic expression in order to simplify the expression we are going to remove the parentheses for number two we have eight and then in parentheses 2 n + 6 now we can't combine those terms in the parentheses so what we can do we can use the distributive property to remove those parentheses and simplify this expression so let's distribute the 8 to the 2 m and to the 6 this gives us 8 * 2 m Plus 8 * 6 8 * 2 m is 16 m + 8 * 6 is 48 now 16m and 48 are unlike terms so we don't have any terms that we can combine so we are done here 16 m + 48 is our simplified expression let's move on to number three where we have S and then in parentheses a minus 9 let's distribute that 7 to the A and to the 9 that gives us 7 * a minus bring the subtraction sign down 7 * 9 7 * a is just 7 Aus 7 * 9 is 63 so we end up with 7 a minus 63 we don't have any like terms that we can combine so we are simplified and done again 7 a - 16 3 now I do want to mention another way to think through this and this is another way to Think Through whenever subtraction or negatives are involved so let me rewrite the expression and then distribute the seven so we have 7 * a which is 7 a and then we can think of that subtraction sign and the nine as a 9 so including the sign in front with the nine so we think of that as a 9 so let's distribute that 7 to the9 7 * -9 is 63 so 63 and we get 7 a minus 63 that way as well and again that's just a different way to Think Through It you get the same thing either way but you can include the sign in front of the term and think of that as A9 so something to keep in mind let's move on to number 4 where we have 10 and then in parentheses -5x - 4 y let's distribute the 10 to the -5x and to the 4 y so 10 * -5x - 10 * * 4 y 10 * -5x gives us50 xus 10 * 4 y gives us 40 y so we end up with 50x - 40 y we don't have any like terms that we can combine so we are done again 50x - 40 y now let's take a look at a different way to think through this so I will rewrite the expression off to the side so let's distribute the 10 to the -5x and then we will think of that as -4 y so include the sign in front of that term 10 * 5x is 50 x and then 10 * -4 Y is 40 y so we get the same thing that way as well - 50x - 40 y so there is an introduction to the distributive property let's take a look at four more examples here are more examples that we can go through to get the distributive property down let's jump into number one where we have 9 and then 3 C + 2 in the parentheses let's distribute that 9 to the 3C and to the two so we have 9 * 3 C which is 27 C plus so we bring that addition sign down and then we have 9 * 2 which is 18 so we end up with 27 C + 18 now we don't have any like terms that we can combine so this has been simp simplified we can't simplify any further so again 27 C + 18 let's move on to number two where we have 4 and then in parentheses -6 y - 5 let's distribute that 4 to the -6 Y and to the 5 so 4 * -6 y is4 y bring the subtraction sign down and then we have 4 * 5 which is 20 so we end up with -4 y - 20 we don't have any like terms that we can combine so this is simplified again -4 y minus 20 now I do want to mention another way to Think Through number two and this is an option when we have subtraction so let me rewrite the expression here and then we need to distribute the four so distribute to the -6 Y and then when we distribute to the five we are going to look at this as five so we are including that subtraction sign the sign in front of the five and look at this as5 this gives us well 4 * -6 Y is -4 Y and then 4 * -5 is -2 so we get -4 y - 20 that way as well so we get the same thing either way just slightly different as far as working through the distributive property let's move on to number three where we have -2 and then in parentheses -8x - 7 y let's distribute the -2 to the -8x and to 7 y so -2 * -8x gives us 16x remember a NE * a Nega is a positive so -2 * -8 is a pos6 and then we have that X then we can bring down the subtraction sign and then we have -2 * 7 y that gives us4 y now this is correct but we can clean this up a little bit so to speak we have a double sign the subtraction and then the negative we don't need both of those signs we can rewrite it with just one think about working with negatives when we subtract a negative that's the same as adding a positive we can change this to addition and that will make this simpler and like I said clean it up a little bit we can rewrite this as 16x plus 14 y we don't have any like terms that we can combine so we are simplified again 16x + 14 y just like number two I'll go through this a slightly different way as far as thinking through the distributive property when it comes to subtraction I will rewrite the expression off to the side here and then we can distribute that -2 to the -8x and then we can distribute that -2 to the -7 y so we are including that sign in front of the term -2 * -8x gives us 16x and then -2 * -7 y gives us a postive 14 y so plus 14 y so we get the same thing there as well lastly let's move on to number four where we have 15 and then 3 G + H in the parentheses so let's distribute that 15 to the 3G and to the H so we have 15 * 3G that gives us 45g plus and then 15 * H well that's just 15h so we end up with 45 G + 15h we don't have any like terms that we can combine so we can't simplify this any further this is simplified so again 45g + 15h so there are the basics of using the distributive property to simplify algebraic expressions let's move on to some examples of algebraic expressions that will need to be simplified using both the distributive property and combining like terms here are four more algebraic expressions that we need to simplify we will use both the distributive property and combining like terms let's jump into number one where we have 4 + 2 and then in parentheses n + 6 now since this expression has parentheses we need to start there do not do 4 + 2 first we still need to consider the order of operations within the parentheses we have n + 6 n and 6 are unlike terms so we can't combine those terms what we can do is Use the distributive property to remove the parentheses and then we can look to combine like terms to simplify the expression further so let's distribute the two to the n and to the the 6 2 * n gives us 2 N and then we have 2 * 6 which gives us a positive 12 so + 12 this is a positive 2 N and then we can bring down that four now that the parentheses have been removed we can look to simplify further by combining like terms 4 and 12 are like terms those are constant terms so we can't and combine them 4 + 12 gives us 16 so our final simplified expression is 2 n + 16 now when we write expressions typically speaking we want any variable terms first and then constant terms go last so that's why we have 2 n + 16 if we end up having multiple terms that involve variables they go in order from greatest to least as far as exponents and then if variable terms have the same exponents go in ABC order so again for number one we just have two terms a variable term and then a constant term so 2N + 16 is our final simplified expression now that final simplified expression is equivalent to the original expression we were just able to simplify that original expression by using the distributive property and combining like terms let's move on to number two where we have 6 and then in parentheses 3x + 5 and parentheses - 9x let's start by using the distributive property to remove the parentheses so let's distribute this 6 to the 3x and to the 5 6 * 3x gives us 18x and then 6 * 5 5 gives us a positive 30 so + 30 then we have minus 9x so a 9x now that we removed the parentheses we can look to combine like terms 18x and -9x are like terms so we can combine them make sure to include the sign that's in front of a term that's 9x so we have 18x - 9x or 18x combined with 9x that gives us a positive 9x and then we have + 30 a positive 30 so our final simplified expression is 9x + 30 let's move on to number three where we have 23 + 3 and then in parentheses 8 y - 10 let's remove the parentheses by using the the distributive property so let's distribute the 3 to the 8 Y and to the -10 3 * 8 y gives us 24 Y and then 3 * -10 gives us 30 this is a positive 24 Y and then bring down the 23 now as far as the distributive property and subtraction we can also think through that as 3 distributed to 8 y so 3 * 8 y that gives us 24 y then we can bring the subtraction sign down and then distribute the 3 to the 10 so 3 * 10 that gives us 30 so 24 Yus 30 we got the same thing thinking through the distributive property that way as well now that we removed the parentheses we can look to combine like terms we have two constant terms 23 and -30 so we can combine those like terms so we have 24 Y and then 23 minus 30 or 23 combined with -30 gives us7 so - 7 our final simplified expression 24 y - 7 lastly let's move on to number four where we have -8 and then in parentheses C minus D and parentheses - 5D let's start by removing the parentheses by using the distributive property distribute the8 to the C and distribute the8 to D -8 * - c gives us a positive 8 C remember a negative * a negative equals a positive -8 * D gives us a positive 8 D and then we have Min - 5D so a5d now that we removed the parentheses we can look to combine like terms 8D and -5 D are like terms so let's combine those like terms we end up with 8 C and then 8D minus 5D or 8D combined with 5D gives us a positive 3D so plus 3D our final simplified expression 8 C + 3D so there's how to use the distributive property and combining like terms to simplify an algebraic expression let's take a look at four more examples and these will get a little more complex here are four more algebraic expressions that we need to simplify using the distributive property and combining like terms these will get a little more complex than the previous four examples let's jump into number one where we have 13 a + 4 and then in parentheses a + 9 now since we have parentheses we need to start there we can't combine the terms in the parentheses they are unlike terms so we can use the distributive property to remove the parentheses once the parentheses are removed we can look to combine like terms so let's distribute that four to the A and to the 9 so we have 4 * a which is 4 a and then 4 * 9 is a positive 36 so plus 36 this is a positive 4 a and then we can bring down 13A now that we removed the parentheses we can look to combine like terms in order to simplify this further so do we have any like terms that we can combine yes 13A and 4 a are like terms so we can combine those terms 13 a + 4 a is 17 a and then we have that positive 36 so plus 36 and this is our final simplified expression 17 a + 36 now that simplified expression is equivalent to the original expression we were just able to simplify that original expression by using the distributive property and combining like terms let's move on to number two where we have five and then in parentheses x ^ 2 - 3 and parentheses + 10 - 4x let's start by using the distributive property in order to remove the parentheses then we can look to combine like terms let's distribute this five to the x^2 and to the -3 5 * x^2 gives us 5 x^2 and then 5 * -3 gives us -5 now another way to think through that distributive property there is to do 5 * x^2 which is 5x^2 bring the subtraction sign down and then do 5 * 3 we get 5x^2 - 15 that way as well just a slightly different way to Think Through the distributive property then we have a positive 10 so + 10 and then a -4x so - 4 4 x now that we removed the parentheses we can look to combine like terms so do we have any like terms that we can combine yes we have two constant terms -15 and 10 so let's combine those like terms so we have 5 x^ 2us 4X that's a -4x the term will take the sign that's in front of it so make sure we have -4x there and then the constant term comes last so we have -15 + 10 or -5 combined with positive 10 that gives us5 so - 5 and this is our final simplified expression 5x^2 - 4x - 5 now I do want to mention as far as how this simplified expression is written typically speaking when writing Expressions the greatest exponent comes first so greatest to least if exponents are the same go in ABC order constant terms go last so we have 5x squar the exponent of two comes first because that's the greatest exponent then we have -4x so that variable has an understood exponent of one remember whenever there is isn't an exponent written there is an understood exponent of one so to the power of one anything to the power of one is just itself and then we have the constant term of -5 last so that's something to keep in mind as far as writing out Expressions let's move on to number three where we have seven and then in parentheses G + 3H and parentheses + 4 and then in parentheses 2 g - 6 h let's start by using the distributive property to remove any parentheses and then we can look to combine like terms let's distribute this 7 to the G and to the 3H so we have 7 * G that gives us 7 G and then we have 7 * 3 H that gives us a positive 21h so plus 21h then we can distribute the 4 to the 2G and to the -6h 4 * 2G gives us a posi 8G so Plus 8 G and then 4 * -6h gives us 24h a positive * a negative equals a negative so 24 H or minus 24h now for this expression I'm going to rewrite it with all of the like terms next to each other this is a strategy we can use to organize the expression and make combining like terms a little simpler since all of the like terms will be right next to each other so let's identify any like terms in this expression we have 7g and 8G and then 21h which I will box in in order to separate and then 248 H let's rewrite this with those like terms next to each other so we have 7 G Plus 8 G + 21 H minus 24h remember that's a 24h now all of the like terms are right next to each other so like I mentioned it's a little simpler to combine the like terms so now we can combine like terms let's start with 7g and 8G 7g + 8G gives us 15 G then we have 21h minus 24h so positive 21h combined with - 24h that gives us3 H so minus 3 H and this is our final simplif ified expression 15 Gus 3H lastly let's move on to number four where we have 18 x - 10 and then in parentheses 2x - 2 y + 9 and parentheses - 6X let's start by using the distributive property to remove the parentheses we're going to distribute -10 we take the sign that's in front so this is -10 we need to distribute to the 2x to the -2 Y and to the 9 -10 * 2x gives us 20 x -10 * -2 y gives us postive 20 y remember a negative * a negative equals a positive and then we have -10 * a POS 9 that gives us990 we then have the -6x and the positive 18x that we need to bring down now we can look for any like terms that we can combine so do we have any like terms yes 18x -2X and -6x let's rewrite the expression with those like terms next to each other so 18x - 20x - 6X + 20 y - 90 now we can combine like terms so we have 18x - 20x - 6X so we are combining a positive 18x a - 20x and a -6x 18x - 20x is -2X -2X - 6X that gives us 8 x then we have + 20 y - 90 so -8x + 20 y - 90 is our final simplified expression so there's how to simplify Al to break expressions by combining like terms and using the distributive property I hope that helped thanks so much for watching until next time peace