# Multiplying Polynomials

After studying this lesson, you will be able to:

• Multiply 2 binomials using the FOIL method
• Multiply any 2 polynomials using the distributive property.

When we multiply 2 binomials, we can use a special version of the distributive property called the FOIL method. Here's what FOIL stands for:

 Example: (x - 4) (y + 3) F irst Terms are multiplied x and y are the First Terms O utside Terms are multiplied x and 3 are the Outside Terms I nside Terms are multiplied -4 and y are the Inside Terms L ast Terms are multiplied -4 and 3 are the Last Terms

The FOIL method is the same as distributing twice. The FOIL method only works when multiplying two binomials.

Example 1

(y + 5) (y + 7)

Since we are multiplying two binomials, let's use the FOIL Method.

1 st: Multiply the First Terms y times y

2 nd: Multiply the Outside Terms y times 7

3 rd: Multiply the Inside Terms 5 times y

4 th: Multiply the Last Terms 5 times 7

This will give us y 2 + 7y + 5y + 35 which simplifies to y 2 + 12y + 35

Note: We would get the same answer if we distributed each term in the first binomial to each term in the second binomial. That would be the same as using the FOIL Method. }{\f1\fs24\cf2

Example 2

(x + 3)(x - 6)

Since we are multiplying two binomials, let's use the FOIL Method.

1 st: Multiply the First Terms x times x

2 nd: Multiply the Outside Terms x times -6

3 rd: Multiply the Inside Terms 3 times x

4 th: Multiply the Last Terms 3 times -6

This will give us x 2 - 6x + 3x - 18 which simplifies to x 2 - 3x - 18

Example 3

( 3x - 5 ) ( 5x + 2 )

Since we are multiplying two binomials, let's use the FOIL Method.

1 st: Multiply the First Terms 3x times 5x

2 nd: Multiply the Outside Terms 3x times 2

3 rd: Multiply the Inside Terms -5 times 5x

4 th: Multiply the Last Terms -5 times 2

This will give us 15x 2 + 6x - 25x - 10 which simplifies to 15x 2 - 19x - 10

Example 4

( 5a + 1) ( 5a - 1 )

Since we are multiplying two binomials, let's use the FOIL Method.

1 st: Multiply the First Terms 5a times 5a

2 nd: Multiply the Outside Terms 5a times -1

3 rd: Multiply the Inside Terms 1 times 5a

4 th: Multiply the Last Terms 1 times -1

This will give us 25a 2 - 5a + 5a -1 which simplifies to 25a 2 - 1

Example 5

(2x - 5)(3x 2 - 5x + 4)

This time we are multiplying a binomial by a trinomial so we cannot use the FOIL Method. Instead, we will distribute each term in the binomial to each term in the trinomial.

1 st: Multiply 2x times the trinomial

2 nd: Multiply -5 times the trinomial

This will give us: 6x 3 - 10x 2 + 8x - 15x 2 + 25x - 20 which simplifies to 6x 3 - 25x 2 + 33x - 20

Example 6

(x - 2)(x 2 - x - 1)

This time we are multiplying a binomial by a trinomial so we cannot use the FOIL Method. Instead, we will distribute each term in the binomial to each term in the trinomial.

1 st: Multiply x times the trinomial

2 nd: Multiply -2 times the trinomial

This will give us: x 3 - x 2 - 1x - 2x 2 + 2x + 2 which simplifies to x 3 - 3x 2 + x + 2