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Mastering Polynomial and Monomial Multiplication: Key Concepts and Examples

In this lesson, we will explore how to multiply a polynomial by a monomial using the distributive property. You will learn to apply this method through various examples, including practical problems like calculating the dimensions of a dog run based on its perimeter. We will work through guided practice problems and prepare for a mid-test to reinforce your understanding. Essential vocabulary and step-by-step examples will aid in mastering this topic. Let's dive into multiplying polynomials and monomials effectively!

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Mastering Polynomial and Monomial Multiplication: Key Concepts and Examples

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  1. Lesson 13-4Pages 683-686 Multiplying a Polynomial by a Monomial

  2. What you will learn! • How to multiply a polynomial by a monomial.

  3. Vocabulary

  4. What you really need to know! The distributive property can be used to multiply a polynomial by a monomial.

  5. Example 1: Find the product: -8(3x + 2) -8(3x) + -8(2) -24x + -16 -24x – 16

  6. Example 1b: Find the product: (6x – 1)(-2x) (6x)(-2x) – (1)(-2x) -12x2− -2x -12x2 + 2x

  7. Example 2: Find the product: 4b(-a2 + 5ab + 2b2) 4b(-a2) + 4b(5ab) + 4b(2b2) -4a2b +20ab2 + 8b3

  8. Example 3: The length of a dog run is 4 feet more than three times its width. The perimeter of the dog run is 56 feet. What are the dimensions of the dog run?

  9. w = width 4 + 3w = length Perimeter = 2(L) + 2(w) 56 = 2(w) + 2(4 + 3w) 56 = 2w + 8 + 6w

  10. 56 = 2w + 8 + 6w 56 = 8w + 8 48 = 8w 6 = w Width = 6, Length = 22

  11. Page 685 Guided Practice #’s 4-10

  12. Read: Pages 683-684 with someone at home and study examples!

  13. Homework: Pages 685-686 #’s 12-30 even #’s 33-46 all

  14. Prepare for Mid-Test! Pages 698-699 #’s 9-40 Odd Answers in Back of Book!

  15. Page 756 Lesson 13-4

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