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Lesson 8-1 Multiplying Monomials

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.

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Lesson 8-1 Multiplying Monomials

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  1. Lesson 8-1Multiplying 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. • 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: (6cd5)(5c5d2) 6 • c • d5 • 5 • c5 • d2 30c6d7

  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 • each base appears exactly once, • 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)

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