this lesson is about polom poly means more than one so we are talking about more than one term so first let's talk about what are like terms so can you add and subtract everything you want to the answer to that that is no you can only add and subtract like terms so now the question is what makes something a like term so as we look at these terms on the board we want to see if we can group The like terms together the way that you can tell something a like term is if it has the same letters with the same exponents the numbers in the front can be different but the letters and the exponents have to be exactly the same so if we we look at this 5x his like term is the 3x they are like terms I could add them or subtract them um if I looked at the 7even Y his like term is the 4 y I could add or subtract them together if I look at the 8xy his like term is the 5x y they are like terms because they both have an X and they both have a y um if I look at the 9x squar his like term would be the 2x^2 um sad little four right here doesn't have any like terms because there are no no other terms up here that just have a number with no letters so now that we know what like terms are we're going to see if we can add and subtract some together when you add and subtract like terms you only add and subtract the numbers in the front you do not touch the X's or the A's or the B's or the powers you only decide that they are like terms and then you add the numbers in the front so if I look at number one I have 2X + 5x yes they are like terms because they both have an X I can add them together and we know that 2 + 5 is 7 so that gives me 7 x not 7 x^ squared do not add powers when you add your like terms again you are just adding the numbers in the front so looking at number two they are like terms because they both have an A and A B and the a is squared on both of them so I can add these together and a three and a -7 is going to give me a -4 and then the back end stays exactly the same number three they are not all like terms if you'll notice this one has a power of a three but this term has a power of a two and he has a power of a two so while they all have X's they are not all like terms this guy right here has no buddies he has no like terms so we just bring him down but then I can combined this one and this one because they are like terms please keep in mind that that negative applies to that four so that's a -4 plus a 7 which is going to give me a posi3 x squared the the back end of the term is kind of like its last name last name does not change just the numbers in in the front so I'm looking at number four I've got terms 4 a and a9a again that negative goes to that nine those are my like terms if I add a four and a negative 9 that gives me a ne5 a and then I have a -6b and a positive 2 B and that gives me a -4b and the last example we have a this uh to find my like terms I have a positive 5x I have a - 3x and I have a NE 9x so the five and the -3 is going to give me a -2 and then to combine the -2 with the --9 would give me a -1x and then I've got a positive 8 and a -10 and that gives me a minus two okay so now I have um two polom I have this one which has three terms in it and this one which has three terms in it and I want to add them together so I'm going to add my like terms so I have a 5x squar and there's a number in front of this it's a one you don't have to write it but if it helps you you can so I have a 5x2 and a 1 X2 so that's six x^2 then I have this -3x and this POS 4X which are like terms and so that would give me a positive 1 x and again you can put the one in front of the X but you don't have to and then I have this positive one and this -6 which are like terms which would give me A5 also notice how I wrote my answer it has the X squ term in the front and then the X to the first Power and then the term that doesn't have an X that's called descending order which is how you're going to see most of your answers written so in looking at number seven I look at my y squar term and he has a like term right here so that'd be 3 y s + 7 y^ 2 which is 10 y^ 2 and then I have a positive 5 Y and if you'll look and look carefully you'll see that he doesn't have any like terms so I'm just going to bring him down POS 5 Y and then I have this -6 and that -9 and when I add those together that gives me a NE 15 and again my final answer is in descending order with my second power and then my first power and then my term that doesn't have a y okay these are the ones that are really simple but students miss these a lot because they don't take the time to change their signs so with this minus sign in between this minus applies to everything that's in these parentheses so what you're going to want to do is change this to a plus sign and then you change the sign of every term in the parentheses after it including the first term so he now becomes a negative he now becomes a negative and he is now positive and now it's an addition an addition problem just like we had been doing so we find our like terms so I have a 5x SAR and a - 1x^2 so that's 4x2 I have a -3x and a NE -4x so it gives me -7x and I have a one and a positive 6 which gives me a positive 7 same thing on number nine I'm going to take the time to walk through and change my signs because I don't want to miss this problem so I'm going to change that to a plus sign change the three to a minus change this plus to a minus and change the five to a positive and then I'm going to add my like terms but you've got to be really careful because this and this are not like terms and it's really easy to get in the habit of always just adding those first two but he has a power of a three and he has power of a two they're not like terms this 2x cubed right here has no buddies he has no other body that has a an X Cub term so we're just going to bring him down then I go to my X squ term that's his like term so I have a - 4x^2 and a - 3x^2 so that gives me -7 x^2 now I could move on to this positive seven here but if you'll notice in your answer you you have to the third power and to the second power so think about what term should be next it should be the X to the first power so instead of doing this one I'm going to come over here and do this term next because he is an x to the 1 and he has no like term so I'm just going to bring him down Min - 2x then I'm going to add my positive 7 and my positive five and get a positive 12 okay on number 10 I'm going to change the minus to a plus change all the signs in the second princ and combine my like terms so he is like terms with this guy so that's a three and a -7 which gives me a -4 y^ 2 he has no like terms so I'm going to bring him down and then I have a -6 and a positive 9 which is a positive3 okay so now we're going to start by multiplying so this is Distributing this five is buted up against these parentheses which means we need to distribute it when Distributing is multiplying you do not have to have like terms to be able to multiply you can multiply anything you only have to have like terms to be able to add or subtract so when I distribute 5 * 2x gives me 10 X and 5 * the -9 gives me a -45 these are not like terms I cannot combine them so that's my final answer on number 12 I'm going to distribute the three but I'm only going to distribute it to the items that are in the parentheses this minus two is just hanging out waiting for me to finish Distributing so when I distribute my three that's going to give me a 12x and then a minus 21 and then I bring down my minus two and a lot of students will walk away from a problem like this and they're not done we have like terms that we can combine now I don't have any like terms for the 12x so I'm just going to bring him down but I can combine the - 21 and the -2 and get a -23 now on number 13 a lot of students look at this and they say oh I'm going to distribute the five but that five is not buted up against those parentheses that's not what we are Distributing we are Distributing this negative and if you want to put a one right there you can if it helps this five is just hanging out and I distribute my NE -1 so -1 * 3x gives me a -3x and a - 1 * a ne5 gives me a positive five now I want to look and see if I have any like ter terms and I do I have a positive five and a positive five but if you'll remember we said we wanted to put our answers in descending order so I'm going to start with the X term and put him in the front you guys know that that negative it belongs to this three so -3x and again this is a positive five and another positive five so that gives me a + 10 on number 14 the only thing that we are Distributing is the next -2 make sure you take that negative with it so the 15 is just hanging out distribute the -2 so -2 * 4 gives me a 8 a -2 * a 3X gives me a -6 x and then what is this five doing he's just hanging out now that I've done my Distributing now I'm going to combine my like terms but I'm going to have a heads up and I'm going to look for my descending order so I really want the -6x to go first and then I'm going to combine my 15 and my8 and my positive five so 15 and a negative 8 is going to give me a seven and 7 + 5 it's going to give me a positive 12 okay in number 15 the 8X is just hanging out I'm Distributing not just a four but a NE 4 so when I distribute -4 to 2x that gives me a - 8X and a-4 * a -3 is a positive2 again I want to go in descending order I'm going to start with my x's so I have a positive 8X and a negative 8X they cancel and all I have left is a 12 so now we're going to try to take a word problem and just write an equation that represents that word problem so John has $36 in a savings account he plans on depositing $20 into the account each month and not taking any money out of the account write a function rule that will give the total amount he has in the account T after any number of months in so T represents the total amount he has in the account so T equals and then think about it okay so how much money did he start with he started with $36 so he has a flat $36 sitting in the bank now he's decided that he wants to deposit $20 into the account each month and not take any out so we are adding to this $36 $20 but not just one time he said that he wants to deposit $20 into the account each month and it says after any number of months in so n represents the number of months so 20 times n that way if it was two months you would just plug a two in there if it was three months you would plug a three in there and that would give you 60 bucks and then you would add it to the $36 if he was going for four months you would plug a four in there and four * 20 gives you 80 and then you would add the 80 to the 36 so this shows that he is depositing $20 per month where n represents the number of months this is how much he had in the bank to start with so this equation represents how much he has in the bank at any given time it's got the $36 he started with and then the20 $20 per month Suzanne was given $100 for a graduation gift she also got a job this summer and is babysitting for $15 per hour assuming she doesn't spend any of the money write a function rule that will give the total amount she has a after any number of hours H babysitting okay a is my total amount so a equals and what did she start with she started with a hundred bucks somebody gave her $100 for graduation plus she is going to add two that $15 per hour and we don't know how many hours she's going to work but however many hours that is it's $15 each time and we add it together because it adds to her savings the local cable company in Walnut Cove charges $120 activation fee for all new accounts they also charge $45 per month for cable service write a function for the charges after any number of months of service so charges equal will they charge you 120 bucks up front just to set it up then they're also going to charge you $45 per month so 120 bucks to set it up plus $45 per month that equals the total of the charges Sam earned $3,000 this summer working in his dad's store his parents are making him pay for his car insurance he will have to pay $60 each month write a function of how much money Sam has given that he is paying his car insurance each month okay so this one he earned $3,000 this summer so he has $3,000 but he has to pay 60 bucks each month right a function of how much money he has M so money Sam has $3,000 he earned it this summer working he has got $3,000 but out of that he has to pay for his car insurance so he loses $60 per month notice that it's a subtraction sign and not an addition sign I'm not adding to the money that Sam has I'm subtracting away from the money that Sam has Fitness United gy charges a $100 Initiation fee plus $25 per month for membership muscles R Us Jim charges $75 in Initiation fee plus $30 per month for membership write a function that represents the difference and the cost between the fitness United membership and the muscles RS membership so I want the fitness United minus muscles are us difference means minus so I need to set up an equation for Fitness United and I need to set up an equation for muscles are us so let's see Fitness United charges a $100 Initiation fee plus $25 per month $100 Initiation fee plus $25 per month muscles R Us only charges $75 uh for your Initiation fee but they're going to charge you $30 per month so there are my two equations and it wants me to find the difference okay we'll think back to about 15 minutes ago when we talked about this minus in between here change it to a plus and change the sign of everything in the parentheses that follows it and now I add my like terms well I have a 100 and I have a - 75 and I have a positive 25 M and a - 30m and then some you may be saying well that's not in the right order we put the M first if you're going to do that then the negative has to go with it because that negative belongs to that five so -5 M plus 25 either one of these answers would be fine Sprint charges $35 per month for cell phone services plus 10 cents per minute for phone calls Verizon charges $50 per month but only charges $5 cents a minute for phone calls write a function that represents the difference when you get to problems like this I'd really like to see you circling that word difference so we're going to do Sprint minus Verizon so give me an equation for Sprint well they charge $35 per month plus now be careful with this don't write 10 this is 10 cents per minute minus Verizon charges $50 per month but they only charge 5 cents per minute again the decimals are really important right here okay and again we talked about it with the minus sign we're going to change it to a plus change the sign of both these guys behind it and then I'm going to add my like terms so I have a 35 and a 50 so it's going to be a -5 all right now be careful here I have a positive 10 cents and a NE 5 cents so that's going to give me a positive 5 cents M and again if you wanted to put the m in the front this positive stays with it so 0.05 M Min - 15 either one of those would be just fine