[Music] welcome to math with Mr J in this video I'm going to cover how to simplify algebraic expressions we will Use the distributive property and we will combine like terms in order to do so 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 4 a and then we can bring down 13 a 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 17A 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 end parentheses + 10 - 4x let's start by using the distributive property in order to remove the parentheses then we can look to combin 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 15 now another way to think through that distributive property there is to do 5 * x^2 which is 5 x^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 - 4x 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^ 2- 4X that's a -4x the term will take the sign that's in front of it so make sure we have -4 X there and then the constant term comes last so we have -5 + 10 or15 combined with postive 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 typic Al 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^2 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 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 S and then in parentheses G + 3 H and parentheses plus 4 and then in parentheses 2 G - 6h let's start by using the distributive property to remove any parentheses and then we can look to combin 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 * 3H that gives us a positive 21h so plus 21h then we can distribute the four to the 2 G and to the -6h 4 * 2 G gives us a positive 8 G so Plus 8 G and then 4 * -6h gives us 24h a positive time a negative equals a negative so4 H or - 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 24h let's rewrite this with those like terms next to each other so we have 7 G Plus 8 G + 21 H minus 24 H 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 8 G 7 G + 8 G gives us 15 G then we have 21h minus 24h so positive 21h combined with4 H that gives us3 H so - 3H and this is our final simplified expression 15 G minus 3H lastly let's move on to number four where we have 18x - 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 * a negative equals a positive and then we have -10 * a postive 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 20x and -6x let's rewrite the expression with those like terms next to each other so 18x - 20x - 6x+ 20 Yus 90 now we can combine like terms so we have 18x - 20x - 6X so we are combining a positive 18x a 20x and A6 X 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 you have it there's how to simplify algebraic expressions and we used both the distributive property and combining like terms I hope that helped thanks so much for watching until next time peace