1. Lesson 8-1 Multiplying Monomials

2. 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.

3. 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.

4. Vocabulary  Monomial

5. Vocabulary  Monomial - a number, a variable, or a product of a number and one or more variables.  Constant

6. Vocabulary  Monomial - a number, a variable, or a product of a number and one or more variables.  Constant – A Number

7. 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.

8. 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.

9. 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.

10. 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.

11. Product of Powers Words: To multiply two powers that have the same base, add the exponents. Example:

12. Example 2 Simplify: (6cd 5 )(5c 5 d 2 ) 6 c d 5 5 c 5 d 2 30c 6 d 7

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

14. Example 3 Simplify:

15. Power of a Product Words: To find the power of a product, find the power of each factor. Example:

16. Example 4 Simplify:

17. 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.

18. Example 5 Simplify:

19. Example 6 Simplify:

20. Homework Pg 413 16 – 40 (even) 43 – 45 (all)