Understanding SOAP and Cube Roots

This video tutorial teaches how to factor the sum and difference of two cubes. It begins with an introduction to the necessary formulas and the importance of recognizing perfect cubes. The SOAP acronym is introduced to help remember the signs in the formulas. The video then provides four detailed examples, demonstrating the step-by-step process of factoring different expressions involving cubes. The tutorial emphasizes the importance of identifying the greatest common factor and using the correct formula for either the sum or difference of cubes.

What is the cube of 2?

• 8

• 10

• 6

• 4

Which of the following is a perfect cube?

• 27

• 50

• 9

• 16

What does the 'S' in the SOAP acronym stand for?

• Subtract

• Same

• Square

• Simplify

In the SOAP acronym, what is the sign of the last term always?

• Opposite

• Same

• Positive

• Negative

What is the cube root of 27?

• 2

• 3

• 4

• 5

What is the factored form of x^3 - 27?

• (x + 3)(x^2 + 3x + 9)

• (x - 3)(x^2 + 3x + 9)

• (x + 3)(x^2 - 3x + 9)

• (x - 3)(x^2 - 3x + 9)

What is the cube root of 8y^3?

• 4y

• 2y

• y

• 8y

What is the factored form of 8y^3 + 1?

• (2y + 1)(4y^2 - 2y + 1)

• (2y - 1)(4y^2 + 2y + 1)

• (2y + 1)(4y^2 + 2y + 1)

• (2y - 1)(4y^2 - 2y + 1)

What is the cube root of 64d^3?

• 16d

• 4d

• 8d

• 2d

What is the factored form of 216c^3 + 1000d^3?

• (6c + 10d)(36c^2 + 60cd + 100d^2)

• (6c - 10d)(36c^2 + 60cd + 100d^2)

• (6c - 10d)(36c^2 - 60cd + 100d^2)

• (6c + 10d)(36c^2 - 60cd + 100d^2)