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Multiplying Monomials and/or Binomials and FOIL - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

This problem I’m going to solve by using the FOIL process. FOIL isn’t an official Math word like you guys probably think of tinfoil which makes sense like that’s in a real world where we use the word FOIL. In Math, FOIL or the letters F-O-I-L is an acronym.

F stands for multiplying the first terms of each binomial. O stands for the outer terms, I is the inner terms and l stands for the last terms. So don’t think like FOIL is like an official Math process, it’s just a way that teachers often teach their students to remember how to do this like double distributing process. Here is what it look like.

First I’m going to multiply my first terms. 3x times x, 3x times x is my first which gives me the product 3x². Next I’m going to multiply my outers. 3x is on the outside, and also on the outside is 4. 3x times 4, those are my outers, that’s going to give me 12x. Next I’m going to do my inners, inners mean the inside numbers, 1 times x which is just plain old x. You don’t need to write the one, it’s like implied. And then I’m going to do my lasts. The last term in the parentheses here is 1, here I have 4. That product of 1 times 4 gives me +4. So this represents product of my first, product of my outers, products of my inners, products of my lasts.

And then the final step here is to combine like terms. 12x plus 1 more x is 13x, so here is my final answer; 3x² plus 13x plus 4. FOIL is just a handy way to help you remember what’s going on with distributing. Here is what it looks like officially. This 3x is getting multiplied by the x and the 4, and then also what I did is this 1 got multiplied by the x and by the 4. It’s like a double distributing process and then you go through and combine them at the end.

So again FOIL is an acronym. The letters stand for first, outers, inners, last, but it only works for the products of 2 binomials.

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