1. Multiplying Polynomials
Math I
Unit 2 Day 2

2. Vocabulary
An area model for polynomial arithmetic is a way to visually represent multiplying two polynomials using geometry.
A volume model for polynomial arithmetic is a way to visually represent multiplying three polynomials using geometry.

3. Multiplying a monomial and a polynomial
Find the product

4. Find the product

5. Find the Product

6. Multiplying Polynomials using the area of the polynomial shown
You know that the area of a rectangle is the product of its length and width. In the model, let 3x + 1 represent the length and let x + 2 represent the width. To find the total area of the model, add the areas of each rectangular part. x x x 1 x x2 x2 x2 x
X + 2 1 x x x 1 x x x 1 1 x

7. The dimensions of a rectangle are y + 9 and 2y + 3. Draw an area model
The dimensions of a rectangle are y + 9 and 2y Draw an area model. Then write an expression for the area of the rectangle.

8. Multiplying Polynomials
Find the Product

9. Multiplying Polynomials
Find the Product

10. Practice 1. 2.

11. Practice 3. 4.

12. Multiplying Polynomials using a Volume Model
Write a polynomial for the volume of the rectangular prism shown.
You know that the volume of a rectangular prism is the product of its length, width, and height. In the figure shown, let x represent the length, x + 1 represent the width and x + 2 represent the height.
x + 2 x
x + 1

13. Practice Problem
The dimensions of a rectangle are x, x + 8, x Write an expression for the volume of the prism.

14. The square of a binomial pattern

15. The square of a binomial pattern
a. (7x + 2)2
b. (3x – 2)2

16. The square of a binomial pattern
Practice Problems

17. Sum and Difference Patterns

18. Sum and Difference Patterns
a. (m + 9)(m – 9)
b. (4n – 3)(4n + 3)

19. Sum and Difference Patterns
Practice Problems