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

2. Bellwork Simplify each expression 1.(x)(3x) 2.(2y)(4y) 3.(t 2 )(6t) 4.(4m)(m2) Solutions 3x 2 6t 3 8y 2 4m 3

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 a 2

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 - 2a 2 (- 3a) 1.Multiply the coefficients to get 6 6 2. Multiply the variables to get a 3 a3a3 3. Multiply the signs – negative times negative = positive + In this example the solution is +6a 3

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) 6x 2 – 18x 2. Then multiply 3x times – 6 to get – 18x 1. Multiply 3x times 2x to get 6x 2 6x 2 – 18x is the solution

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

12. Your Turn In the notes section of your notebook write and multiply the polynomial by the monomial. 1.(5y – 4)3 2.(3x – 7)4x 3.-5( 3x 2 – 7x + 9) Solutions 15y - 12 -15x 2 + 35x - 45 12x 2 – 28x

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)