Multiply the polynomials using FOIL. (x−5)(x−12)\left(x-5\right)\left(x-12\right)(x−5)(x−12)

x 2 − 17 x + 60 x^2-17x+60 x 2 − 17 x + 60

Multiply the polynomials using FOIL. ( x − 5 ) ( x − 12 ) \left(x-5\right)\left(x-12\right) ( x − 5 ) ( x − 12 )

Everyone, so in this problem here, we have these 2 polynomials, x minus 5 and x minus 12, and we're gonna multiply them. Now because these are 2 binomials, this is 2 terms and 2 terms, we can do so by using the foil method. So let's go ahead and get started here. Remember, the foil method means that we're gonna do first and first. That's the f. So, really, this just becomes x squared. That's my f. Then I do the outside terms. The outer outside terms are this and this over here. So it's the x and the 12. However, it's really important when you have minus signs, you're gonna multiply the x and not just 12. You have to also borrow the sign that's in front of this. So it's x times negative 12. You always use the sign that's in front of the number here. Alright? That's super important. So this just becomes not 12 x, but negative 12 x or minus 12 x. That's the outside terms. Now let's do the same thing with the inside terms. Same thing over here. This is not 5 times x. It's negative 5 times x. Always use the sign that's in front. So this is now minus 5 x, and that's the inner terms. And then finally, we use the last two terms. That is gonna be the negative 5 and the negative 12. So that's gonna be these two terms over here. Same thing. Use the negatives. This is negative 5 times negative 12, and this becomes positive 60. So that's oil, first, outer, inner, and last. Alright. Now we just simplify. This just becomes x squared minus actually, let's do this in black. Let's do x squared. Let's do negative 12 x and negative 5 x combined. These things will combine to negative 17 x, and then here we have positive 60 over here. So this expression over here is simplified as possible it can't combine any more like terms, and that's how you foil these kinds of expressions. So whenever you see negative signs, just be really careful you always have to use that negative sign. Thanks for watching.