Multiplying Polynomials

Be able to use different methods to multiply two polynomials.

FHS Polynomials 2

Multiplying Polynomials

• To multiply polynomials together each term of the first polynomial must be multiplied by each term of the second polynomial.

• There are several methods for multiplying polynomials.

• The three methods we will be using are the box method, using the memory device FOIL, and using the distributive property.

FHS Polynomials 3

The Box Method

• The simplest method for multiplying polynomials is to use a box or a chart to fill in. Here is an example:

2 5 3 4x x 2x 5 3x 4

26x 15x

208x

26 15 8 20x x x

26 7 20x x

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How does FOIL work?

• Look at the example below to show FOIL at work:

F = multiply the first term in each binomialO = multiply the two outside terms togetherI = multiply the two inside terms togetherL = multiply the last term in each binomial

(x + 6)(2x +3)

· + · + · + ·

= 2x2 + 3x + 12x + 18 = 2x2 + 15x + 18

x 2x6 32x6 3x

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The Distributive Method

• The third method is to use the distributive property to multiply each term of the first polynomial by each term of the second polynomial. You must use this method or the box method if you are multiplying polynomials that are not binomials.

23 5 2 4x x x 2 23 2 4 5 2 4x x x x x 3 2 23 6 12 5 10 20x x x x x 3 23 11 22 20x x x

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Let’s Practice

1. (y – 5)(y – 1) =

y2 – y – 5y + 5 =

y2 – 6y + 5

2. (3xy + 4)(4xy – 5) =

12x2y2 – 15xy + 16xy – 20

12x2y2 + xy – 20

3. (5 – x)(5 + x) =

25 + 5x – 5x – x2 =

25 – x2

4. (y + 2)2 =

(y + 2)(y + 2) =

y2 + 2y + 2y +4 =

y2 + 4y + 4