Section 7.8

Section 7.8 Multiplying Polynomials

FOIL FOIL

FOIL FOIL

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.

California Standards

Multiply.Let’s Try Multiplying Monomials

A. (6y3)(3y5) (6y3)(3y5)

18y8

Group factors with like bases together.

B. (3mn2) (9m2n) (3mn2)(9m2n)

27m3n3

Multiply.

Group factors with like bases together.

Multiply.

(6 3)(y3 y5)

(3 9)(m m2)(n2 n)

3(x + 7) = 3(x) + 3(7) = 3x + 21

-2(-3 + 4y) = -2(-3) + -2(4y) = 6 + -8y

Review of Distributive Property

Multiplying Monomials and Polynomials 4(3x2 + 4x – 8)

4 (3x2 + 4x – 8)

(4)3x2 + (4)4x – (4)8 12x2 + 16x – 32

Distribute 4.

Multiply.

FOIL

FOIL(2x + 1)(x – 5)

(3x - 5)(2x + 7) FOIL

FOIL(3x - 5)(2x + 7)

The box method

12x2

18x

20x

30

12x2 + 38x + 30

The box method

18x2

-12x

3x

-2

18x2 - 9x - 2

The box method

8x2

-4x

-12x

6

8x2 - 16x + 6

The box method

20x3 15x2 -10x

-16x2

20x3 - x2 - 22x + 8

-12x 8

Multiply.Challenge

(x – 5)(x2 + 4x – 6)

(x – 5 )(x2 + 4x – 6)

x(x2 + 4x – 6) – 5(x2 + 4x – 6)

x(x2) + x(4x) + x(–6) – 5(x2) – 5(4x) – 5(–6)

x3 + 4x2 – 6x – 5x2 – 20x + 30

x3 – x2 – 26x + 30

Distribute x and –5.

Distribute x and −5 again.

Simplify.

Combine like terms.

Practice Problems • Fill in the blank.

1. (5a + 2)(6a – 1) = a2 + 7a – 2

2. (2x + 9)(x + 2) = 2x2 + x + 18

3. (x + 3)2 = x2 + + 9

30

13

6x

Match1. (4x + 3)(3x + 2)

2. (2x + 8)(6x + 2)

3. (12x + 3)(x + 1)

4. (6x + 4)(2x + 4)

A. 12x2 + 15x + 3

B. 12x2 + 52x + 16

C. 12x2 + 32x + 16

D. 12x2 + 17x + 6

D

B

A

C

Find Each Product(x + 2)(x + 5)

(2x + 1)(x + 2)

(2y + 1)(3y + 4)

(2x + 3)(x + 5)

(10x + 10)(2x + 2)

(x + 7)2

1.

2.

3.

4.

5.

6.

x2 + 7x + 10

2x2 + 5x + 2

6y2 + 11y + 4

2x2 + 13x + 15

20x2 + 40x + 20

x2 + 14x + 49

Lesson Quiz

Multiply.

1. (6s2t2)(3st)

2. 4xy2(x + y)

3. (x + 2)(x – 8)

4. (2x – 7)(x2 + 3x – 4)

5. 6mn(m2 + 10mn – 2)

6. (2x – 5y)(3x + y)

4x2y2 + 4xy3

18s3t3

x2 – 6x – 162x3 – x2 – 29x + 28

6m3n + 60m2n2 – 12mn

6x2 – 13xy – 5y2