Algebra 1

7.7 Multiplying Polynomials

Learning Targets

Language GoalStudents should be able to read, write, say, and classify polynomials.

Math GoalStudents should be able to multiply polynomials.

Essential QuestionWhat information can you gather after multiplying polynomials?

Warm-up

Multiplying Monomials

What are monomials?Polynomial with only one term

Multiplying Monomials- Group factors with like bases together. Then multiply.

Example Type 1: Multiplying Monomials

MultiplyA. B.

Example Type 1: Multiplying Monomials

MultiplyC.

Example Type 2: Multiplying a Polynomial by a Monomial

Multiplying a Polynomial by a Monomial-Use the Distributive Property!

Example Type 2: Multiplying a Polynomial by a Monomial

A. 5(2x + x + 4) B. 2x y(3x – y) C. 4a(a b + 2b )2

Example 3:Multiplying Binomials

• -There are a couple different methods you decide what is best for you.

• You can use the distributive property twice.• You can foil.• You can use the box method.

Multiplying Binomials

• Method 1: Apply the Distributive Property twice (can box)

(x+3)(x+2)

Multiplying BinomialsMethod 2: FOIL METHOD (x+3)(x+2)

First Outer Inner Last Combine like terms/Simplify

Example Type 3: Multiplying Binomials

• Multiply using any methodA. B. C.

Example 4: Multiplying Polynomials

• Again there are multiple ways to solve. Find the way that you like and use it!!

• Distributive Property• Rectangular Model• Vertical Model

Example 4: Multiplying Polynomials

Method 1: Distributive Property(5x + 3)( + 10x – 6)

Example 4: Multiplying Polynomials

Method 2: Rectangular Model(5x + 3)( + 10x – 6)

Example 4: Multiplying Polynomials

Method 3: Vertical Model(5x + 3)( + 10x – 6)

Example Type 4: Multiplying Polynomials

A. (x + 2)(x² – 5x + 4) B. (3x – 4)(-2x² + 5x – 6)

Example Type 4: Multiplying Polynomials

A. (x + 2)(x² – 5x + 4) B. (3x – 4)(-2x² + 5x – 6)

Example Type 4: Multiplying Polynomials

C. D.

Example Type 5: Word Application

A. The length of a rectangle is 5 inches greater than the width.1. Write an expression for the width of the rectangle.

2. Write an expression for the length of the rectangle. 3. Write a simplified expression for the area of the rectangle. 4. Find the area of the rectangle when the width is 3 inches.

5. Find the area of the rectangle when the length is 9 inches.

Example Type 5: Word Application

B. The length of a rectangle is 4 meters shorter than its width. 1. Write a polynomial that represents the area of the rectangle.

2. Find the area of the rectangle when the width is 6 meters.

Lesson Quiz