1. In this lesson, we will multiply polynomials

2. First, we will multiply polynomials with algebra tiles
(x + 2)(x – 3)

3. Model each binomial with Algebra Tiles
(x + 2)(x – 3)

4. Place one binomial on top of the rectangle and the other on the left side
(x + 2)(x – 3)

5. Fill in the rectangle
(x + 2)(x – 3)

6. Remove the factors
(x + 2)(x – 3)

7. Simplify the Solution
x2 – 3x + 2x – 6

8. The simplified solution
x2 – x – 6

9. Multiply coefficients and add exponents
To multiply polynomials, we must first understand properties of exponents
(2x3)(3x2)
To multiply monomials
Multiply coefficients and add exponents
(2xxx)(3xx)
6xxxxx
6x5

10. To multiply monomials and polynomials, we will use the distributive property
3x2(2x – 5)
6x3 – 15x2

11. To multiply binomials, we can use a box
(2x + 1)(3x – 5)

12. Place one binomial on top of the box and one on the left side
(2x + 1)(3x – 5)
2x +1 3x -5

13. Multiply and fill in the box
(2x + 1)(3x – 5)
2x +1 3x -5
6x2 3x
-10x -5

14. Simplify the product in the box
6x2 + 3x – 10x – 5
6x2 – 7x – 5
2x +1 3x -5
6x2 3x
-10x -5

15. Simplify
(3x – 1)2
To square a binomial, place the binomial on the top and left side of the box
3x - 1 3x -1

16. Multiply (3x – 1)2 9x2 – 3x – 3x + 1 9x2 – 6x + 1-1
9x2
-3x 1

17. Complete Activity 9b Use the distributive property
Use Properties of Exponents
Use algebra tiles to multiply polynomials
Use the Box Method to multiply polynomials