Factoring Sum and Difference of Cubes

This video tutorial explains how to derive and apply the formulas for factoring the sum and difference of cubes using long division. It begins with the derivation of the sum of cubes formula, followed by an example of factoring x^3 + 64. The tutorial then covers the derivation of the difference of cubes formula and concludes with an example of factoring 8x^3 - 27.

What is the primary method used in this lesson to factor a sum or difference of cubes?

• Completing the square

• Long division

• Partial fraction decomposition

• Synthetic division

When performing long division for a sum of cubes, what is the first step?

• Multiply the divisor by the dividend

• Add zero terms for missing terms in the dividend

• Subtract the divisor from the dividend

• Divide the dividend by the divisor

In the sum of cubes formula, what is the expression for the trinomial factor?

• a^2 + 2ab + b^2

• a^2 - ab + b^2

• a^2 + ab + b^2

• a^2 - 2ab + b^2

How can x^3 + 64 be expressed using the sum of cubes formula?

• (x + 4)(x^2 - 4x - 16)

• (x + 4)(x^2 + 4x + 16)

• (x + 4)(x^2 + 4x - 16)

• (x + 4)(x^2 - 4x + 16)

What is the cube root of 64 in the context of the sum of cubes?

• 2

• 3

• 4

• 5

What is the first step in deriving the difference of cubes formula?

• Subtract the divisor from the dividend

• Divide the dividend by the divisor

• Add zero terms for missing terms in the dividend

• Multiply the dividend by the divisor

In the difference of cubes formula, what is the expression for the trinomial factor?

• a^2 + ab + b^2

• a^2 - ab + b^2

• a^2 + 2ab + b^2

• a^2 - 2ab + b^2

Which of the following is a factor of a^3 - b^3?

• a - b

• a^2 + ab + b^2

• a + b

• a^2 - ab + b^2

How can 8x^3 - 27 be expressed using the difference of cubes formula?

• (2x - 3)(4x^2 - 6x + 9)

• (2x - 3)(4x^2 + 6x - 9)

• (2x - 3)(4x^2 + 6x + 9)

• (2x - 3)(4x^2 - 6x - 9)

What is the cube root of 27 in the context of the difference of cubes?

• 2

• 3

• 4

• 5