Let's Review. Adding and Subtracting Polynomials. Remember that Combining Like Terms is an application of the Distributive Property.

Transcription

1 Let's Review Adding and Subtracting Polynomials. Combining Like Terms Remember that Combining Like Terms is an application of the Distributive Property. 2x + 3x = (2 + 3)x = 5x 3x 2 + 2x 2 = (3 + 2)x 2 = x 2 2x x x 2 x + 5 x 2 + 3x + 5 This means addition, NOT multiplication! (4x 2 3x + 2 ) + ( 3x 2 + x 4) 4x 2-3x + 2-3x 2 + x - 4 x 2-2x - 2

2 ( 3x 2-2x + 4 ) + ( -2x 2 + 6x + 5 ) 1) Distinguish the like terms ( 3x 2-2x + 4 ) + ( -2x 2 + 6x + 5 ) 2) Group the like terms 3x 2-2x 2-2x + 6x

3 ( 3x 2-2x + 4 ) + ( -2x 2 + 6x + 5 ) 3) Combine the like terms 3x 2-2x 2-2x + 6x x 2 + 4x 9 + How can we model this subtraction? (2x 2 + 4x 5) (x 2 + 2x 3) Hint: Remember that when you subtract, you are actually adding the opposite! (2x 2 + 4x - 5) + (-x 2-2x + 3) x 2 + 2x - 2

4 (n 12) (n 2 + n + 9) n n 2 - n - 9 -n 2-21 Distribute the negative, then combine like terms. Now lets complicate it a little. (n 3) 2(n 2 4n + 5) n - 3-2n 2 + 8n n 2 + 9n - 13

5 Now lets complicate it a little more. 4(n 3) 2(n 2 4n + 5) + 8 4n n 2 + 8n n n - 14 Multiplying a Monomial by a Polynomial (with more than one term) Use the Distributive Property. 2x(x 2 + 3x - 6) 2x 3 + 6x 2-12x

6 Multiplying a Binomial by a Binomial Use the Distributive Property. (2x - 5)(3x + 8) 2x(3x + 8) - 5(3x + 8) 6x x - 15x x 2 + x - 40 (f + 2) 2 (f + 2)(f + 2) f(f + 2) + 2(f + 2) f 2 + 2f + 2f + 4 f 2 + 4f + 4 What's the difference?? Addition (m 2-4) + (m 3 + 2m 2-7m + 3) Multiplication (m 2-4)(m 3 + 2m 2-7m + 3)

7 n[(n + 2)(n 2) 4] Find the degree. 5m 2 n 3 3x 3 y + xy 4

8 Do Now Use Eraser to check the Problem Set

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10 Use Eraser to check the Lesson 9 Generating Polynomials Multiply Polynomials Student Outcomes Students understand that the product of two polynomials produces another polynomial; students multiply polynomials.

11 Classwork Exercise 1 (15 minutes) er Answer What do you notice about the terms along the diagonals in the rectangles you drew?

12 Answer What do you notice about the terms along the diagonals in the rectangles you drew? Answer What do you notice about the terms along the diagonals in the rectangles you drew?

13 Encourage students to recognize that in parts b and c the terms along the diagonals were all like terms, however, in part d one of the factors has no x term. Allow students to develop a strategy for dealing with this, concluding with the suggestion of inserting the term +0x, for a model that looks like the following: Students may naturally ask about the division of polynomials. This topic will be covered in Grade 11, Module 1. The extension challenge at the end of the lesson, however, could be of interest to students inquiring about this. Could we have found this product without the aid of a geometric model? What would that look like? Use the Distributive Property and collect like terms. Also remind students that variables are placeholders for numbers. If x = 5 then the right side is= 270 and the 5 1 of "that quantity" or 5 of that quantity minus 1 of that quantitty

14 Exercise 2 (5 minutes) Students work independently then compare with a neighbor. Discuss and justify. Exercise 3 (10 minutes) Give students 10 minutes to complete Exercise 3 and compare their with a neighbor. Answer

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17 Exercise 4 (5 minutes) Answer

18 Answer Answer Problem Set

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21 (a + b)(a + b) (a + 1)(a + 1) (3 + b)(3 + b)

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