Lesson 8-1 Multiplying 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.

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.

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

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

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

Example 3 Simplify:

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

Example 4 Simplify:

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:

Example 6 Simplify:

Homework Pg – 40 (even) 43 – 45 (all)