MULTIPLYING MONOMIALS

Chapter 8.1

Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems

Students will know how to apply the laws of exponents when multiplying monomials.

MULTIPLYING MONOMIALS

Example 1- Simplify: x2 * x3

Remember: x2 = x * x which can also be written as xx

x2 = x * x and x3 = x * x * x Therefore x2 * x3 = (x*x)*(x*x*x) = xx * xxx =

xxxxx There are 5 x’s in the answer Therefore x2 * x3 = x5

Rule: When multiplying monomials you must add the exponents together. Xm * xn = xm+n

MULTIPLYING MONOMIALS

1. 33 * 34

2. x3 * x4

3. x5(x3)

4. x7(x-2)

MULTIPLYING MONOMIALS

Now you try!

1. 33 * 34

2. x3 * x4

3. x5(x3)

4. x7(x-2)

MULTIPLYING MONOMIALS

Now you try!37

x7

x8

x5

Example 2- Simplify (2x3)(3x4) Multiply the numbers together first: 2 * 3 =

6 Multiply the variables together second: x3 *

x4 = x7

Put the numbers and letters back together for your answer: 6x7

Rule: When multiplying monomials you multiply the numbers and letter separately

MULTIPLYING MONOMIALS

1. 3x3 * 4x2

2. 5x4(2x3)

3. -2x2(4x)

4. -7x(-3x3)

MULTIPLYING MONOMIALS

Your Turn!

1. 3x3 * 4x2

2. 5x4(2x3)

3. -2x2(4x)

4. -7x(-3x3)

MULTIPLYING MONOMIALS

Your Turn!12x5

10x7

-8x3

21x4

Example 3- Simplify (-2x2y3)(3x5y2)

Multiply the numbers together first: –2 * 3 = -6

Multiply the x’s separately: x2 * x5 = x7

Multiply the y’s separately: y3 * y2 = y5

MULTIPLYING MONOMIALS

MULTIPLYING MONOMIALS

(-2x2y3)(3x5y2)

-6 x7y5

1. 3x3y2 * 4x2y2

2. 5x4y3(2x3y4)

3. -2x2y2(4xy)

4. -7xy(-3x3y3)

MULTIPLYING MONOMIALS

More for you12x5y4

10x7y7

-8x3y3

21x4y4

Example 4 Simplify (x3)2

Remember, (x3)2 = (x3) * (x3) = xxx * xxx Therefore (x3)2 = x6

Rule: When a monomial with an exponent is then raised to an exponent you multiply the exponents together. (Xm)n = xm*n

You can always write out x3 twice and add the exponents

MULTIPLYING MONOMIALS

1. (x2)3

2. (x4)4

3. (x3)7

MULTIPLYING MONOMIALS

Practice Makes Perfect!

1. (x2)3

2. (x4)4

3. (x3)7

MULTIPLYING MONOMIALS

Practice Makes Perfect!x6

x16

x21

Example 5 Simplify: 2x2(3x3)2

Remember order of operations, exponents come before multiplication!

Also, any number squared means to multiply it by itself Therefore: 2x2(3x3)(3x3) Multiply the numbers: 2 * 3 * 3 = 18 Multiply the variables: x2 * x3 * x3 = x8

Put the numbers and letters back together: 18x8

MULTIPLYING MONOMIALS

Combination Problems

1. 2x2(3x3)2

2. (4x3)2(2x5)

3. (3x4)3(2x3)2

MULTIPLYING MONOMIALS

One more try

1. 2x2(3x3)2

2. (4x3)2(2x5)

3. (3x4)3(2x3)2

MULTIPLYING MONOMIALS

One more try18x8

108x18

32x11

1. x2 * x3

2. 3x(2x3)3. -2x3(4x4)4. (x4)3

5. 2x3(3x4)2

MULTIPLYING MONOMIALS

Quiz 8.1

1. x2 * x3

2. 3x(2x3)3. -2x3(4x4)4. (x4)3

5. 2x3(3x4)2

MULTIPLYING MONOMIALS

Quiz 8.1x5

6x4

x12

-8x7

18x11