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(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
Assignment
1.
2.
3.
4.
5.
6.
7.
8.
7x3(2x + 3)
3x2(2x2 + 9x – 6)
xy2(x2 + 3xy + 9)
2m2(6m3 + 14m2 – 30m + 14)
(x – y )(x2 – xy + y2)
(2x + 5y)(3x2 – 4xy + 2y2)
(x3 + x2 + 1)(x2 – x – 5)
(4x2 + 3x + 2)(3x2 + 2x – 1)
Reflection – Left Side
• Write about one way you think we might use
multiplying polynomials while studying
quadratic functions.