Homework Help: Mathematics: Algebra: FOIL

The FOIL Method is a process used in algebra to multiply two binomials. The lesson on the Distributive Property, explained how to multiply a monomial or a single term such as 7 by a binomial such as (4 + 9x).

But, what if there was a binomial instead of a single term outside of the parentheses? That is, what if a binomial was being multiplied by another binomial? An example of this is given below.

This is where the FOIL Method comes in.

FOIL Method

FOIL stands for:

First - Multiply the first term in each set of parentheses
Outer - Multiply the outer term in each set of parentheses
Inner - Multiply the inner term in each set of parentheses
Last  - Multiply the last term in each set of parentheses

Now let's give it a try in our problem. We'll start by multiplying the first term in each set of parentheses and then marking down the answer below the problem.

Now we will multiply the outer terms and again mark down the answer below the problem.

And the Inners.

And finally the last terms.

Now as you can see the results from the multiplying of the two inners and the two outers are like terms. Our last step is to combine these like terms. We see that 6x + 42x = 48x, thus

FOIL Method

The FOIL Method cannot always be used to multiply two sets of parentheses. This is the case with the problem below.

The second set of parentheses has 3 terms instead of two. For this, we will use another method.

First, split the problem by multiplying each term in the left polynomial by the entire second polynomial as shown below.

Then use the distributive property to simplify each.

Finally, combine like terms.

Homework Help: Mathematics: Algebra

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