Algebra

10.2 Multiplying Polynomials

Consider a rectangular house

It is 12 feet wide by 18 feet long OK...... it’s a small house.......

12

18

12

18

What is the area of this small house?

12

x 18

216

It is 216 square feet.

12

18

Let’s add interior walls to the house to make 4 rooms

10 8

10

2

12

18

What is the square footage of each room?

10 8

10

2

100 80

1620

Does it still add up to 216 ?

100802016

216

YES

12

18

So the total product is equal to the sum of the smaller products.

10 8

10

2

100 80

1620

100802016

216 =

12

x 18

216

….and we can multiply the dimensions horizontally like this….

(10 + 8) (10 + 2)

100+ 20 +80 +16

= 216 12

1810 8

10

2

100 80

1620

x + 2

x + 8

Let’s do something “crazy” and

x 8

x

2

x² 8x

162x

say that 10 = x.

….and we can multiply the dimensions horizontally like this….

(x + 8) ( x + 2)

x² + 2x +8x +16

= 216

Put the 10 back for x and check

x + 2

x + 8x 8

x

2

x² 8x

162x

= x² + 10x + 16

= (10)² + 10(10) + 16

Multiplying Polynomials

When multiplying polynomials, you use the distributive property. Each term in one polynomial gets multiplied by each term in the other polynomial.

When a binomial is multiplied by another binomial, we refer to the pattern as “FOIL”

FOILStands for:

(x + 8) ( x + 2)

First

x²+ 2x + 8x + 16

= x² + 10x + 16

Outside Inside Last

Try these

(x + 7) (x – 3)

(3x + 4)(x – 5)

(2x – 5)(x – 3)

(x + 3)(x – 3)

x²+ 4x - 21

3x²- 11x - 20

2x²- 11x + 15

x²- 9

It works the same for multiplying binomials by other

polynomials.

(3x + 2)(x² – 5x + 3)

3x³- 15x² + 9x + 2x²- 10x + 6

3x³- 13x²- x + 6

When you multiply a 2 by 3 you get 2 x 3 = 6 terms

Then combine like terms

Homework

pg. 587 # 19 - 47 odd, 54-55, 62-73