Multiplying Polynomials December 1, 2014 Pages 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(x 2 + 4x + 16)  -4(x 2 + 4x + 16)  x(x 2 + 4x + 16) – 4(x 2 + 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)  12x 2 – 8x + 3x – 2  12x 2 – 5x – 2

Example 2 (x + 2)(x 2 + 3x – 1)  x(x 2 + 3x – 1) + 2(x 2 + 3x – 1)  x 3 + 3x 2 – x + 2x 2 + 6x – 2  x 3 + 5x 2 + 5x – 2

Example 3 xy(5x 2 + 8x – 7)  5x 3 y + 8x 2 y – 7xy

Example 4 (3x – 2y)(2x 2 + 3xy – y 2 )  3x(2x 2 + 3xy – y 2 ) – 2y(2x 2 + 3xy – y 2 )  6x 3 + 9x 2 y – 3xy 2 – 4x 2 y – 6xy 2 + 2y 3  Combine Like Terms:  6x 3 + 5x 2 y – 9xy 2 + 2y 3

Assignment 1.7x 3 (2x + 3) 2.3x 2 (2x 2 + 9x – 6) 3.xy 2 (x 2 + 3xy + 9) 4.2m 2 (6m m 2 – 30m + 14) 5.(x – y )(x 2 – xy + y 2 ) 6.(2x + 5y)(3x 2 – 4xy + 2y 2 ) 7.(x 3 + x 2 + 1)(x 2 – x – 5) 8.(4x 2 + 3x + 2)(3x 2 + 2x – 1)

Reflection – Left Side Write about one way you think we might use multiplying polynomials while studying quadratic functions.