Multiplying Polynomials

December 1, 2014Pages 40 – 41 in Notes

Warm-Up – Left Side• Simplify. (Distribute and Combine Like Terms if

possible) x(2x – 1) 3(2x – 1) x(2x – 1) + 3(2x – 1) x(x2 + 4x + 16) -4(x2 + 4x + 16) x(x2 + 4x + 16) – 4(x2 + 4x + 16)

Objective

• add, subtract, and multiply polynomials.[7B]

Essential Question

How will multiplying polynomials help me with quadratic functions?

Multiplying polynomials is…

• just like creating multiple distributions, doing the distributions, and then combining like terms to simplify.

• “Like” terms = exact same variables to the exact same powers.

• Combine by adding the coefficients.

How do we do this?

• Multiply each term in the first polynomial by all terms in the second.

Example 1

• (4x + 1)(3x – 2) 4x(3x – 2) + 1(3x – 2) 12x2 – 8x + 3x – 2 12x2 – 5x – 2

Example 2

• (x + 2)(x2 + 3x – 1) x(x2 + 3x – 1) + 2(x2 + 3x – 1) x3 + 3x2 – x + 2x2 + 6x – 2 x3 + 5x2 + 5x – 2

Example 3

• xy(5x2 + 8x – 7) 5x3y + 8x2y – 7xy

Example 4

• (3x – 2y)(2x2 + 3xy – y2) 3x(2x2 + 3xy – y2) – 2y(2x2 + 3xy – y2) 6x3 + 9x2y – 3xy2 – 4x2y – 6xy2 + 2y3

Combine Like Terms: 6x3 + 5x2y – 9xy2 + 2y3

Assignment1. 7x3(2x + 3)2. 3x2(2x2 + 9x – 6)3. xy2(x2 + 3xy + 9)4. 2m2(6m3 + 14m2 – 30m + 14)5. (x – y )(x2 – xy + y2)6. (2x + 5y)(3x2 – 4xy + 2y2)7. (x3 + x2 + 1)(x2 – x – 5)8. (4x2 + 3x + 2)(3x2 + 2x – 1)

Reflection – Left Side

• Write about one way you think we might use multiplying polynomials while studying quadratic functions.