Factoring Differences of Cubes

The video tutorial explains how to factor a sum or difference of cubes using specific formulas. It begins with an example problem, 8x^3 - 27, and checks for common factors. The tutorial then identifies the expression as a difference of cubes and applies the appropriate formula, where a is 2x and b is 3. The factors are simplified to a binomial (2x - 3) and a trinomial (4x^2 + 6x + 9).

What is the first step in factoring a sum or difference of cubes?

• Multiply the terms together.

• Divide by the greatest common divisor.

• Apply the quadratic formula.

• Check for a common factor other than one.

Which of the following is a characteristic of a difference of cubes?

• The terms are perfect squares.

• The terms are perfect cubes.

• The terms are prime numbers.

• The terms are even numbers.

In the expression 8x^3 - 27, what is the value of 'a' in the factoring formula?

• 27

• 2x

• 8x

• 3

What is the binomial factor of the expression 8x^3 - 27?

• 2x + 3

• 4x^2 + 6x + 9

• 2x - 3

• 8x^3 - 27

What is the trinomial factor of the expression 8x^3 - 27?

• 8x^3 - 27

• 2x - 3

• 4x^2 + 6x + 9

• 2x + 3