Multiplying Polynomials

1
Multiplying Polynomials
2
Multiplying Polynomials

• When multiplying polynomials there are two ways
  to organize your work
• FOILFirst Outer Inner Last (the distributive
  property).
• Multiply the first number in the first
  parentheses by both (or all) numbers in the
  second set of parentheses.
• Multiply the second number in the first
  parentheses by both (or all) numbers in the
  second set of parentheses.
• Combine like terms.

3
Example 1 - FOIL

• Multiply (2x 5)(x 4)
• Multiply 2x by x and 2x by 4
• 2x² and 8x
• Multiply 5 by x and 5 by 4
• 5x and 20
• Now you have 2x² - 8x 5x 20
• Combine like terms (-8x and 5x)
• -3x
• 2x² - 3x 20

4
The Box

• Create a box that has dimensions determined by
  the two polynomials being multiplied. (A
  binomial multiplied by a binomial would need a
  two by two box.)
• Write the polynomials on the outside of the box
  with one term by each of the smaller boxes
• Fill in the boxes by multiplying the two terms on
  the outside of each box.

5
Example 1 - The Box

• Multiply (2x 5)(x 4)
• Draw a 2 by 2 box and put 2x 5 along the top
  and x 4 on the left side.
• To fill in the top left box, multiply 2x and x
• To fill in the top right box, multiply 5 and x
• To fill in the bottom left box, multiply 2x and
  -4
• To fill in the bottom right box, multiply 4 and 5

6
The Box -- Continued

• Combine like terms (-8x and 5x is 3x)
• 2x² - 3x - 20

7
Try these

• 5x2y(2xy3 y)
• (2x 3)(5x 1)
• (x 6)(x 6)
• (x 3)2
• (4x 7)(3x 5)
• (x 1)(2x 2 5x 3)
• (a b)(a b)(b a)

• 10x3y4 5x2y2
• 10x2 13x 3
• x2 36
• x2 6x 9
• 12x2 41x 35
• 2x3 - 3x2 - 2x 3
• -a3 a2b ab2 b3