Factoring Cubes and Trinomials

This video tutorial explains how to factor sums and differences of cubes using specific formulas. It covers two main formulas: one for x^3 - y^3 and another for x^3 + y^3. The video provides detailed examples of factoring 64x^3 + 125 and 27y^3 - 8, demonstrating the application of these formulas. The tutorial concludes with tips on remembering these formulas, emphasizing their importance in calculus and precalculus.

What is the formula for factoring a difference of cubes?

• (x - y)(x^2 - xy + y^2)

• (x + y)(x^2 + xy + y^2)

• (x + y)(x^2 - xy + y^2)

• (x - y)(x^2 + xy + y^2)

How does the formula for factoring a sum of cubes differ from that of a difference of cubes?

• The signs in the binomial and trinomial are reversed.

• The exponents are different.

• There is no difference.

• The variables are swapped.

What is the first step in factoring 64x^3 + 125?

• Rewrite as (2x)^3 + 10^3

• Rewrite as (16x)^3 + 1^3

• Rewrite as (8x)^3 + 25^3

• Rewrite as (4x)^3 + 5^3

What is the result of squaring 4x in the example 64x^3 + 125?

• 64x^2

• 4x^2

• 8x^2

• 16x^2

What is the final trinomial when factoring 64x^3 + 125?

• 16x^2 - 20x + 25

• 16x^2 + 20x + 25

• 16x^2 - 20x - 25

• 16x^2 + 20x - 25

What number cubed gives 27 in the example 27y^3 - 8?

• 9

• 6

• 3

• 2

What is the first step in factoring 27y^3 - 8?

• Rewrite as (27y)^3 - 1^3

• Rewrite as (y)^3 - 8^3

• Rewrite as (9y)^3 - 4^3

• Rewrite as (3y)^3 - 2^3

What is the result of squaring 3y in the example 27y^3 - 8?

• 9y^2

• 27y^2

• 3y^2

• 6y^2

What is the final trinomial when factoring 27y^3 - 8?

• 9y^2 + 6y - 4

• 9y^2 + 6y + 4

• 9y^2 - 6y + 4

• 9y^2 - 6y - 4

Where might you encounter these formulas again?

• In statistics

• In calculus or precalculus classes

• In basic arithmetic

• In geometry