Sum of Cubes and Factoring

The video tutorial explains how to factor the sum and difference of cubes using specific formulas. It begins by identifying the greatest common factor, then applies the sum of cubes formula to factor expressions like 64x^3 + 27y^6. The process involves recognizing the cubes of terms, applying the formula, and simplifying the resulting binomial and trinomial factors.

What is the first step in any factoring problem?

• Apply the difference of cubes formula

• Simplify the expression

• Check for the greatest common factor

• Identify the sum of cubes

Which of the following represents the cube of 4X?

• 16x^2

• 64x^3

• 4x^3

• 8x^3

In the sum of cubes formula, if a = 4X and b = 3y^2, what is the binomial factor?

• 4x - 3y^2

• 16x^2 + 9y^4

• 12xy^2

• 4x + 3y^2

What is the trinomial factor derived from the sum of cubes formula in this example?

• 16x^2 + 12xy^2 + 9y^4

• 16x^2 + 12xy^2 - 9y^4

• 16x^2 - 12xy^2 + 9y^4

• 16x^2 - 12xy^2 - 9y^4

What is the final simplified form of the expression using the sum of cubes formula?

• 4x - 3y^2 and 16x^2 + 12xy^2 - 9y^4

• 4x - 3y^2 and 16x^2 - 12xy^2 + 9y^4

• 4x + 3y^2 and 16x^2 - 12xy^2 + 9y^4

• 4x + 3y^2 and 16x^2 + 12xy^2 + 9y^4