Sum and Difference of Two Cubes

Question 1

What is the formula for the sum of two cubes?

Answer 1

a³ + b³ = (a + b)(a² - ab + b²)

Question 2

What is the formula for the difference of two cubes?

Answer 2

a³ - b³ = (a - b)(a² + ab + b²)

Question 3

How do you identify the values of a and b in a sum or difference of cubes?

Answer 3

Look for terms that are perfect cubes, where a and b are the cube roots of each term.

Question 4

What is the structure of the binomial and trinomial in the sum of cubes formula?

Answer 4

The binomial is (a + b) and the trinomial is (a²- ab + b²).

Question 5

What is the structure of the binomial and trinomial in the difference of cubes formula?

Answer 5

The binomial is (a - b) and the trinomial is (a²+ ab + b²).

Question 6

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

Answer 6

Identify whether each term is a perfect cube.

Question 7

When should you use the sum of cubes formula?

Answer 7

Use it when the expression is in the form a³ + b³.

Question 8

When should you use the difference of cubes formula?

Answer 8

Use it when the expression is in the form a³ - b³.

Question 9

Factor 8x³+ 27 using the sum of cubes formula.

Answer 9

8x³+ 27 = (2x + 3)(4x²- 6x + 9).

Question 10

Why is it helpful to recognize sum and difference of cubes?

Answer 10

It allows you to simplify complex expressions by factoring them into simpler terms.