Exercise 28 Page 502

The FOIL method is a mnemonic for remembering how to multiply two binomials. The word FOIL is an acronym for the words First, Outer, Inner, and Last. Consider, for example, the following product. (x+6)(3x-2) These two binomials can be multiplied by following the next five steps.

Multiply the First Terms

Start by multiplying the first terms of each binomial. In this case, multiply x by 3x. ( x+6)( 3x-2) = x( 3x) The empty box is there as a reminder that there are still missing terms.

Multiply the Outer Terms

Next, multiply the outer terms, that is, multiply the first term of the left-hand side binomial by the second term of the right-hand side binomial. In this case, multiply x by -2. ( x+6)(3x - 2) = x(3x) + x( -2)

Multiply the Inner Terms

Now, multiply the inner terms, that is, multiply the second term of the left-hand side binomial by the first term of the right-hand side binomial. In this case, multiply 6 by 3x. (x+ 6)( 3x-2) = x(3x) + x(-2) + 6( 3x)

Multiply the Last Terms

Next, multiply the last terms of each binomial, that is, multiply the second term of the left-hand side binomial by the second term of the right-hand side binomial. In this case, multiply 6 by -2. (x+ 6)(3x - 2) = x(3x) + x(-2) + 6(3x) + 6( -2)

Simplify

Finally, perform each product and combine like terms, if any, to simplify the resulting expression.

The following applet illustrates the FOIL method using two arbitrary binomials.

Like any other polynomial multiplication, the FOIL method is based on the Distributive Property.