Warm-up: Simplify.1. 6 (3x - 5) =

18x - 30

2. 4 (2x + 10) =

8x + 40

3. 9y - 3y =

6y

4. 7a + 4b + 3a - 2b =

10a + 2b

5. 4 (3x + 2) + 2 (x + 3) =

14x + 14

Multiplying PolynomialsObjective:

•Multiply two monomials

•Multiply a monomial by a polynomial

Why are the following not monomials?

x + yaddition

division

2 - 3a

subtraction

x

y

Multiplying MonomialsWhen multiplying monomials, you

ADD the exponents.

1) x2 • x4

x2+4

x6

2) 2a2y3 • 3a3y4

6a5y7

Simplify m3(m4)(m)

1. m7

2. m8

3. m12

4. m13

Power of a PowerWhen you have an exponent with an

exponent, you multiply those exponents.

1) (x2)3

x2• 3

x6

2) (y3)4

y12

Simplify (p2)4

1. p2

2. p4

3. p8

4. p16

Power of a ProductWhen you have a power outside of the

parentheses, everything in the parentheses is raised to that power.

1) (2a)3

23a3

8a3

2) (3x)2

9x2

Simplify (4r)3

1. 12r3

2. 12r4

3. 64r3

4. 64r4

Power of a MonomialThis is a combination of all of the other

rules.

1) (x3y2)4

x3• 4 y2• 4

x12 y8

2) (4x4y3)3

64x12y9

Simplify (3a2b3)4

1. 12a8b12

2. 81a6b7

3. 81a16b81

4. 81a8b12

add the exponents!

1) Simplify: 5(7n - 2)

Use the distributive property.

5 • 7n

35n - 10

Review: When multiplying variables,

- 5 • 2

3(8 12)

4a a 2) Simplify:

6a2 + 9a

3) Simplify: 6rs(r2s - 3) 6rs • r2s

6r3s2 - 18rs

38

4a a

312

4a

- 6rs • 3

4) Simplify: 4t2(3t2 + 2t - 5)

12t4

5) Simplify: - 4m3(-3m - 6n + 4p)

12m4

+ 8t3 - 20t2

+ 24m3n - 16m3p

6) Simplify: (27x2 - 6x + 12)

16x3 - 28x2 + 4x

Fooled ya, didn’t I?!? Ha! Ha!

Here’s the real answer!

-9x3 + 2x2 - 4x

x3

Simplify 4y(3y2 – 1)

1. 7y2 – 1

2. 12y2 – 1

3. 12y3 – 1

4. 12y3 – 4y

Simplify -3x2y3(y2 – x2 + 2xy)

1. -3x2y5 + 3x4y3 – 6x3y4

2. -3x2y6 + 3x4y3 – 6x2y3

3. -3x2y5 + 3x4y3 – 6x2y3

4. 3x2y5 – 3x4y3 + 6x3y4