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Mastering Polynomial and Monomial Multiplication: Bellwork and Strategies

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ocean-peterson
14 diapositives · 278 Views · Oct 31, 2014

In today's lesson, we focus on multiplying polynomials by monomials using the distributive property. We begin with a bellwork exercise to simplify expressions, and then move into strategies for effective multiplication. Key concepts include recognizing the differences between multiplication and addition of polynomials, and using a step-by-step approach to minimize errors. Examples illustrate how to apply these strategies, leading to practice problems for students to complete. Remember, it's essential to show all work for credit in your assignments!

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  1. MJ2A Ch 13.4 – Multiplying a Polynomial by a Monomial

  2. Bellwork • Simplify each expression • (x)(3x) • (2y)(4y) • (t2)(6t) • (4m)(m2) Solutions 3x2 8y2 6t3 4m3

  3. Assignment Review • Text p. 680 # 10 – 25

  4. Before we begin… • Please take out your notebook and get ready to work… • In the last two lessons we looked at adding and subtracting polynomials… • In today’s lesson we will look at multiplying a polynomial by a monomial… • We will use the distributive property here…you are required to recognize and know how to work with the distributive property!

  5. Objective 13.4 • Students will multiply polynomials by monomials

  6. Background Knowledge • At this point you should all know that the rules for multiplying are not the same as adding… • For example you cannot add polynomials unless you have like terms… • That doesn’t apply to multiplying… • I can multiply a ● b to get ab • Also, at this point you should know that if you multiply a ● a you get a2

  7. Strategy • When multiplying monomials and polynomials a good strategy is to segment the parts… • What that means is you do a step by step process doing the coefficients first, then the variables, then the exponents, and finally the sign of the terms… • This strategy is effective because it minimizes errors… • Let’s look at an example…

  8. Example Multiply -2a2 (-3a) • Multiply the coefficients to get 6 2. Multiply the variables to get a3 6 a3 + 3. Multiply the signs – negative times negative = positive In this example the solution is +6a3

  9. Distributive Property • When multiplying a polynomial by a monomial you will use the distributive property… • That is you will multiply what on the outside of the parenthesis with EACH term on the inside of the parenthesis • Let’s look at an example…

  10. Example #1 (2x – 6)(3x) 1. Multiply 3x times 2x to get 6x2 2. Then multiply 3x times – 6 to get – 18x 6x2 – 18x 6x2 – 18x is the solution

  11. Example #2 1. Multiply 3a ● a2 to get 3a3 (3a)(a2 + 2ab -4b2) 2. Then multiply 3a ● 2ab to get + 6a2b 3a3 +6a2b -12ab2 3. Then multiply 3a ● -4b2 to get -12ab2 3a2 + 6a2b – 12ab2 is the solution

  12. Your Turn • In the notes section of your notebook write and multiply the polynomial by the monomial. • (5y – 4)3 • (3x – 7)4x • -5( 3x2 – 7x + 9) Solutions 15y - 12 12x2 – 28x -15x2 + 35x - 45

  13. Summary • In the notes section of your notebook summarize the key concepts covered in today’s lesson • Today we discussed: • Multiplying polynomials by monomials • What methodology will you use? • What strategy will you use?

  14. Assignment • Text p. 685 # 11 – 24 Reminder • This assignment is due tomorrow • I do not accept late assignments • You must show how you got your answer (no work = no credit)