How to factor using the sum of two cubes

The video tutorial covers factoring techniques, focusing on the difference of squares and the sum of cubes. It begins with an introduction to factoring and the difference of squares, followed by a detailed explanation of the sum of two cubes and its formula. The instructor demonstrates how to apply this formula to a specific problem, simplifying the expression step by step. The tutorial emphasizes recognizing cube numbers and using the sum of cubes formula effectively.

What is the factored form of a difference of two squares?

• (a + b)(a + b)

• (a - b)(a - b)

• (a^2 + b^2)

• (a + b)(a - b)

Which of the following is the correct formula for factoring a sum of cubes?

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^3 + b^3 = (a - b)(a^2 + ab + b^2)

• a^3 + b^3 = (a + b)(a^2 + ab + b^2)

• a^3 + b^3 = (a - b)(a^2 - ab + b^2)

How can the number 8 be expressed as a cube?

• 2^3

• 5^3

• 3^3

• 4^3

In the expression 2x^3 + 3y^3, what are the values of A and B when using the sum of cubes formula?

• A = 2x, B = 3y

• A = 3x, B = 2y

• A = 3y, B = 2x

• A = 2y, B = 3x

What is the final factored form of the expression 2x^3 + 3y^3 after applying the sum of cubes formula and factoring out the GCF?

• 2x(2x + 3y)(4x^2 - 6xy + 9y^2)

• 2x(2x - 3y)(4x^2 + 6xy + 9y^2)

• 2x(2x + 3y)(4x^2 + 6xy - 9y^2)

• 2x(2x - 3y)(4x^2 - 6xy - 9y^2)