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# Multiplying binomials

CCSS.Math:

## Video transcript

multiply 3x plus 2 times 5x minus 7 so we're multiplying two binomials and I'm actually going to show you two really equivalent ways of doing this one that you might hear in a classroom and it's kind of a more of a mechanical memorizing way of doing it which might be faster but you really don't know what you're doing and then there's the one where you're essentially just applying something that you already know in kind of a logical way so I'll first do the memorizing way that you might be exposed to and they'll they'll use something called foil foils let me write this down here coil so you could immediately see that whenever someone gives you a mnemonic to memorize that you're doing something pretty mechanical so foil literally stands for first first outside let me write it this way you're right oil oil where F the F in foil stands for first the o n foil stands for outside the I stands for inside and then the L stands for last and the reason why I don't like these things is when you're 35 years old you're not going to remember what foil stood for and then you're not going to remember how to multiply this binomial but let's just apply foil so first says just multiply the first terms in each of these binomials so just multiply the 3x times the 5x so 3x times the 5x the outside part tells us multiply the outside terms so in this case you have 3x on the outside and you have negative 7 on the outside so that is plus 3x times negative 7 the inside the inside well the inside terms here are 2 + 5 X so plus 2 times 5x and then finally you have the last terms you have the 2 and the negative 7 so the last term is 2 times negative 7 2 times negative 7 so what you're essentially doing is just making sure that you're multiplying each term by every other term here where we're essentially doing is multiplying the doing the distributive property twice we're multiplying the 3x times 5x minus 7 so 3x times 5 X minus 7 is 3x times 5x plus 3x minus 7 and we're multiplying the 2 times 5x minus 7 to give us these terms but anyway let's just multiply this out just to get our answer 3x times 5x the same thing as 3 times 5 times X times X which is the same thing as 15 x squared you can use X to the first times X to the first so you multiply the X's you get x squared 3 times 5 is 15 this term right here 3 times negative 7 is negative 21 and then you have your X right over here and then you have this term which is 2 times 5 which is 10 times X so plus 10 X and then finally you have this term here in blue 2 times negative 7 is negative 14 and we aren't done yet we can simplify this a little bit we have two like terms here we have this let me find a new color we have two terms with a X to the first power just an X term right over here so if we have negative 21 of something and you add 10 or another way if you have 10 of something and you subtract 21 of them you're going to have negative 11 of that something and we put the other terms here you have 15 15 x squared and then you have your minus 14 and we are done now I said I would show you another way to do it so I want to show you why the distributive property can get us here without having to memorize foil so the distributive property tells us that if we're looking for multiplying something times an expression you just have to multiply it times every term in the expression so we can distribute we can distribute the 5x onto the 3 or actually we could let me view it this way we could distribute the 5x minus 7 this whole thing onto the 3x plus 2 let's let me just change the order since we're used to distributing something from the left so this is the same thing as 5x minus 7 times 3x plus 2 I just swapped the 2 expressions and we can distribute this whole thing times each of these terms now what happens if i take 5x minus 7 times 3x well that's just going to be 3x times name's 5x minus 7 so I've just distributed the 5x minus 7 times 3x and to that I'm going to add two times 5x minus 7 I've just distributed the 5x minus 7 on to the 2 now if you now we can do this tribute of property again we can distribute the 3x onto the 5x we can distribute the 3x onto the 5x and we can distribute the 3x onto the negative 7 we can distribute the 2 onto the 5x over here and we can distribute the 2 on that negative 7 on that negative 7 now if we do it like this what do we get 3x times 5x that's this right over here if we do 3x times negative 7 that's this term right over here if you do 2 times 5x that's this term right over here if you do 2 times negative 7 that is this term right over here so we got the exact same result that we got with foil now foil can be faster if you just want to do it you kind of can skip to this step I I think it's important that you know that this is how it actually works just in case you do forget this when you're 35 or 45 years old and you're faced with multiplying binomials you just have to remember the distributive property