Multiplying Polynomials (FOIL)

Multiplying Polynomials

Day 1

Multiplying by a monomial

• Distribute the monomial to each of the terms in the parentheses

• Multiply the numbers and add exponents of like variables

• For example: 3x² (4x⁴ -2x³) = 12x⁶ - 6x⁵

• Now you try...

Multiple Choice

8x³(2x⁴ + 7x² - 5x)

• 16x¹² + 56x⁶ - 40x³

• 16x⁷ + 56x⁵ - 40x⁴

• 10x⁷ + 15x⁵ - 13x⁴

• 10x¹² + 15x⁶ - 13x³

Multiple Choice

- 4m²n(3mn - 5m³n⁴)

• - 1m²n + 1m⁶n⁴

• 12m³n² - 20m⁵n⁵

• - 12m³n² + 20m⁵n⁵

• - 7m³n² - 9m⁵n⁵

Multiplying Binomials using FOIL

• FOIL stands for Firsts, Outsides, Insides, Lasts (sometimes this is called double distribution since you take the first term and distribute to the second binomial and then take the second term and distribute to the second binomial)

• Here is an example: (2x - 9)(x + 3)

• = 2x(x) + 2x(3) - 9(x) - 9(3)

• = 2x² + 6x - 9x -27 (now combine like terms)

• = 2x² - 3x - 27

Multiple Choice

(4x + 7)(4x - 7)

• 16x² - 49

• 16x -49

• 16x² + 49

Multiple Choice

(3x + 8y)(2x + 3y)

• 6x² + 25xy + 11y²

• 5x² + 16xy + 11y²

• 6x² + 25xy + 24y²

Find the Volume of a rectangular prism

• Volume = (length)(width)(height)

• If length = 2 and width = 4 and height =5

• V = (2)(4)(5)

• V = 40 units cubed

Multiple Choice

Find the Volume of the rectangular prism whose length is (3m - 2), height is (m + 4), and width is (5m³)

• 15m⁵ + 50m⁴ - 40m³

• 3m² + 10m - 8