Lesson 8-1Multiplying Monomials

Mathematics Standards- Number, Number Sense and Operations: Explain the

effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.

- Patterns, Functions and Algebra: Generalize patterns using functions or relationships and freely translate among tabular, graphical and symbolic representations.

- Patterns, Functions and Algebra: Describe problem situations by using tabular, graphical and symbolic representations.

Mathematics Standards- Patterns, Functions and Algebra: Add, subtract,

multiply and divide monomials and polynomials.

- Patterns, Functions and Algebra: Simplify rational expressions by eliminating common factors and applying properties of integer exponents.

- Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

Vocabulary

Monomial

Vocabulary

Monomial - a number, a variable, or a product of a number and one or more variables.

Constant

Vocabulary

Monomial - a number, a variable, or a product of a number and one or more variables.

Constant – A Number

Example 1

Determine whether each expression is a monomial. Explain your reasoning.

a) 17 – s

This is not a monomial because it involves subtraction, not multiplication.

Example 1

Determine whether each expression is a monomial. Explain your reasoning.

b) ¾

This is a monomial because it is a real number and an example of a constant.

Example 1

Determine whether each expression is a monomial. Explain your reasoning.

c)

This is not a monomial because it is the quotient, not the product, of two variables.

dc

Example 1

Determine whether each expression is a monomial. Explain your reasoning.

d)

This is a monomial because it is the product of a number, , and three variables.

5

8abc

5

1

851abc

Product of Powers

Words: To multiply two powers that have the same base, add the exponents.

Example: 16124124 or aaaa

Example 2

Simplify: (6cd5)(5c5d2)

6 • c • d5 • 5 • c5 • d2

30c6d7

Power of a Power

Words: To find the power of a power, multiply the exponents.

Example: 459595 or kkk )(

Example 3

Simplify: 2332 ])[(2332

182144262,

Power of a Product

Words: To find the power of a product, find the power of each factor.

Example: 333333 8 or 22 yxyxxy

Example 4

Simplify: 253 zy

22523 zy

2109 zy

Simplifying Monomial Expressions

To simplify an expression involving monomials

1)each base appears exactly once,

2)there are no powers of powers, and

3) all fractions are in simplest form.

Example 5

Simplify: 322 34 )()( dcd

323222 34 )()( ddc 622 2716 ddc )(6222716 ddc)(

82432 dc

Example 6

Simplify: 452243 28 )(])[( ghhg

4522422322 28 )( ghhg 4516124 28 )( ghhg

451612 20964 )(, ghhg)(, 45441612 20964 hghg

)(, 2041612 160964 hghg361653665 hg,

Homework

Pg 413

16 – 40 (even)

43 – 45 (all)