Beginning Algebra, 11th Edition

SECTION 5.5 Multiplying Polynomials^331

The product of the binomials is the sum of the four monomial products.

This approach can be extended to polynomials with any number of terms.

OBJECTIVE 3 Multiply binomials by the FOIL method.When multiplying

binomials, the FOIL methodreduces the rectangle method to a systematic approach

without the rectangle. Consider this example.

Distributive property

Distributive property again

Multiply.

Combine like terms.

The letters of the word FOIL originate as shown.

Multiply the First terms: F

Multiply the Outer terms: O

This is the outer product.

Multiply the Inner terms: I

This is the inner product.

Multiply the Last terms: L

The outer product, and the inner product, should be added mentally to get

so that the three terms of the answer can be written without extra steps.

= x^2 + 8 x+ 15

1 x+ 321 x+ 52

5 x, 3 x, 8 x

1 x+ 321 x+ 52 3152.

1 x+ 321 x+ 52 31 x 2.

1 x+ 321 x+ 52 x 152.

1 x+ 321 x+ 52 x 1 x 2.

=x^2 + 8 x+ 15

=x^2 + 3 x+ 5 x+ 15

=x 1 x 2 + 31 x 2 + x 152 + 3152

= 1 x+ 32 x+ 1 x+ 325

1 x+ 321 x+ 52

= 6 x^2 + 7 x+ 2

= 6 x^2 + 4 x+ 3 x+ 2

12 x+ 1213 x+ 22

Multiplying Binomials by the FOIL Method

Step 1 Multiply the two First terms of the binomials to get the first term of

the answer.

Step 2 Find the Outer product and the Inner product and add them (when

possible) to get the middle term of the answer.

Step 3 Multiply the two Last terms of the binomials to get the last term of

the answer.

8 x Add.

5 x

3 x

1 x+ 321 x+ 52

F= x^2 L = 15

I

O