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Understanding Monomials: Multiplication and Division Techniques

In this lesson, we will explore the concepts of multiplying and dividing monomials, essential skills for progressing in algebra. We will review key ideas, including the product of powers property and the quotient of powers property. You will practice using these properties to simplify expressions. Additionally, we will solve polynomial subtraction examples and summarize the main concepts. Be prepared to take notes and complete your assignments as we deepen our understanding of monomials and their operations.

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Understanding Monomials: Multiplication and Division Techniques

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  1. MJ3 Ch 12.6 – Multiplying & Dividing Monomials

  2. Bellwork • Subtract the polynomials • (4x + 10) – (3x + 7) • (5n2 + n – 2) – (3n2 + 2n – 1) Solutions: x + 3 2n2 – n – 1

  3. Assignment Review • Text p. 582 # 12 – 25

  4. Before we begin… • Please take out your notebook and get ready to work… • In the last lesson we looked at subtracting polynomials… • Today we will focus on monomials and how to multiply and divide them • You will need to know how to do this in order to do the next lesson which is multiplying monomials and polynomials

  5. Objective 12.6 • Students will multiply & divide monomials

  6. Quick Review • A monomial is a number, a variable, or the product of a number and one or more variables Examples: 8, 2a, 3xy, 5x2y3

  7. Quick Review • Exponents – a mathematical notation to denote repeated multiplication Example: Exponent 3 6 It means 6●6●6 Base

  8. Product of Powers Property • To multiply powers with the same base you add the exponents Example: 24●23 = 24+3 or 27 Proof: 2 ● 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 27 Caution: It is expected that you know a number or variable with no exponent has an exponent of 1

  9. Multiplying Monomials • You can use the product of powers property to multiply monomials. • The key is that the monomial must have the same base. Example: -3x2 (4x5) = -12x7 1st Do the numbers: 3(4) = 12 2nd Do the signs: Negative times a positive is Negative 3rd Do the exponents: x2(x5) = x2+5 = x7

  10. Your Turn • In the notes section of your notebook write the example and multiply. Express answer with exponents • 93● 92 • y4 ● y9 • -2m(-8m5) Solutions: 95 y13 16m6

  11. Quotient of Powers Property • To divide powers with the same bases, subtract their exponents Example: Proof:

  12. Your Turn • In the notes section of your notebook simplify using the quotient of powers property 1. 2. 3. Solutions: x7 6w4 53

  13. Summary • In the notes section of your notes summarize the key concepts covered in today’s lesson • Today we discussed: • The Product of Powers Property • What do you do to the exponents? • The Quotient of Powers Property • What do you do to the exponents?

  14. Assignments • Text p. 586 # 15 – 30 Reminder • This assignments is due tomorrow • I do not accept late assignments • Write the problem and your answer

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