Module 18.2

Multiplying Polynomial Expressions

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How can you multiply binomials and polynomials?

There are 4 methods; most often you’ll use #1 and #2.

FOIL

FirstOuterInnerLast

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METHOD #1 of 4

We begin by multiplying two binomials together.

F -->O -->I -->L -->

FOIL

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FOIL

(x – 2) (x – 6) = 𝑥2 – 6x – 2x + 12

= 𝑥2 – 8x + 12 Often – but not always.

(3x + 2) (2x – 3)

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Note

(2x + 1) (x – 3) = 2𝑥2 –5x – 3

METHOD #2 of 4

(2x + 1) (x – 3)

= 2𝑥2 + 1x – 6x – 3

= 2𝑥2 –5x – 3

Create a table.

Note:It doesn’t matter which expression is horizontal or vertical.

Your Turn

4x –7

2x

+3

(4x – 7) (2x + 3)

METHOD #3 of 4

2 6

3 2

5 2

7 8

8 3 2

Vertical format, like multiplying multi-digit whole numbers.

Your Turn

2x – 2

3x + 3

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(x – 2) (x – 6) = x(x – 6) –2(x – 6)

= 𝑥2 – 6x – 2x + 12

= 𝑥2 – 8x + 12

Another Example

METHOD #1 of 4

The FOIL Method

Now we multiply a binomial and a trinomial.

Create a table.

Multiplying a binomial and a trinomial

Note:It doesn’t matter which expression is horizontal or vertical. Just be sure there are enough boxes!

METHOD #2 of 4 – USE THIS ONE

We Do

(𝑥4 + 𝑥2 + 1) (x – 4)

METHOD #3 of 4

Vertical format, like multiplying multi-digit whole numbers.

Multiplying a binomial and a trinomial

METHOD #4 of 4 P. 858

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Use FOIL or any other method you prefer

x + 4

x + 1 A = (x + 4) (x + 1)

Use FOIL or any other method you prefer

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30

Orik 20 A = (20)(30) = 600

30 – x

Laura 20 - x A = (20 – x)(30 – x)

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x

x x

x

15

20

(Write a polynomial.)

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