Objective - To multiply polynomials.

Multiply the polynomial by the monomial.

1) 3(x + 4)

2)

3)

6k(2k2 4k 3)

2a(a 5)

3x 12

2a2 10a

12k3 24k2 18k

Distributive Property

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

Make sure to use the signs when you multiply

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

Make sure to use the signs when you multiply

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

Make sure to use the signs when you multiply

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner LastMake sure to use the signs when you multiply

2x

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

Make sure to use the signs when you multiply

5x

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

x2

Make sure to use the signs when you multiply

3x

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

x2

5x

Make sure to use the signs when you multiply

15

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

x2

5x

3x

For use with the product of binomials only!

(x 3)(x 5)

First Outer Inner Last

x2

5x

3x

15

x2 2x 15

Combine Like Terms

Try...

(m 3)(m 6)

First Outer Inner Last

m2

6m

3m

18

m2 9m 18

Greatest Monomial Factor

Factor completely.

1)

2)

3)

4)

12a3 16a2b

x4 y2 x2y5

18a3b 27a2b2 36a2b3

x5 x4 x2

24a ( )3a 4b

2 2x y ( )2x 3 y

29a b( )2a 3b 2 4b

2x ( )3x 2 x 1

Use FOIL to multiply the binomials below.

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

(y 7)(y 4)

(m 2)(m 8)

(x 6)(x 4)

(t 10)(t 6)

(x 4)(x 5)

(x 3)(x 8)

(y 7)(y 9)

(x 2)(x 11)

(2 m)(7 m)

(6 k)(4 k)

2y 11y 28

2m 10m 16

2x 2x 24

2t 4t 60

2x 9x 20

2x 5x 24

2y 16y 63

2x 9x 22

214 5m m

224 10k k

Objective - To recognize Difference of 2 perfect squares

Multiply.

1)

2)

3)

4)

(x 3)(x 3)

(m 7)(m 7)

(y 10)(y 10)

(t 8)(t 8)

Inner and Outer terms cancel!

2x 9 2m 49 2y 100

2t 64

So in this situation you always have the first term squared minus the last term squared

Perfect Square Trinomials

1)

2)

3)

(x 5)2

(m 2)2

(2x 7)2

(x 5)(x 5)

x2 10x 25

(m 2)(m 2)

m2 4m 4

(2x 7)(2x 7)

4x2 28x 49