Factoring and Simplifying Expressions

This video tutorial covers the process of factoring sums and differences of cubes. It begins with an introduction to the necessary formulas, highlighting that these forms are factorable unlike squares. The video explains the patterns of signs in the formulas and verifies them through detailed examples. It provides step-by-step demonstrations of factoring expressions like x^3 - 27, 5x^3 + 625, and 8x^3 - 64, emphasizing the importance of recognizing perfect cubes and factoring out the greatest common factor.

What is the pattern of signs for the sum of cubes?

• Plus, plus, minus

• Minus, plus, plus

• Plus, minus, plus

• Minus, minus, plus

Which of the following is not factorable?

• a^2 - b^2

• a^2 + b^2

• a^3 - b^3

• a^3 + b^3

How many products are obtained when verifying the formula for a^3 + b^3?

• Five

• Four

• Seven

• Six

What is the result of simplifying a^2b - a^2b?

• a^2b

• a^3

• 0

• b^2

What is the binomial factor when factoring x^3 - 27?

• x - 27

• x + 27

• x - 3

• x + 3

What is the trinomial factor when factoring x^3 - 27?

• x^2 + 3x + 9

• x^2 - 3x + 9

• x^2 + 3x - 9

• x^2 - 3x - 9

What is the greatest common factor in the expression 5x^3 + 625?

• 625

• 25

• 5

• 125

What is the binomial factor when factoring 5x^3 + 625?

• 5x - 5

• x + 5

• 5x + 5

• x - 5

What is the greatest common factor in the expression 8x^3 - 64?

• 2

• 4

• 8

• 16

What is the binomial factor when factoring 8x^3 - 64?

• 2x + 2

• x - 2

• x + 2

• 2x - 2