Factoring Sums and Differences of Cubes

This video tutorial explains the process of factoring a sum or difference of cubes. It begins with identifying perfect cubes in expressions and emphasizes the importance of factoring out the greatest common factor (GCF) before applying the sum of cubes formula. The tutorial demonstrates prime factorization to find the GCF and then proceeds to factor the binomial into a binomial and a trinomial. The video concludes with a complete factorization of the expression, highlighting that the resulting trinomial is not further factorable.

What is the main challenge in the given example of factoring a sum or difference of cubes?

• The numbers are too small.

• The expression involves high powers.

• The expression is already factored.

• The numbers are not perfect cubes.

Why is it important to factor out the greatest common factor first?

• It is not important.

• It simplifies the expression.

• It ensures the expression is factored correctly.

• It makes the numbers larger.

What is the greatest common factor of 64 and 216?

• 8

• 6

• 4

• 12

How many factors of 2 are there in the prime factorization of 64?

• 6

• 5

• 4

• 3

What is the result of factoring out the greatest common factor from the expression?

• 64x^3 + 216y^3

• 8x^6 + 27y^3

• 64x^6 + 216y^3

• 8x^3 + 27y^3

Why is 8x^6 considered a perfect cube?

• It cannot be written as a cube.

• It can be written as (8x)^3.

• It can be written as (4x)^3.

• It can be written as (2x^2)^3.

What is the value of 'A' in the sum of cubes formula for this example?

• 2x

• 2x^2

• 3y^2

• 3y

What is the binomial factor in the factored expression?

• 2x + 3y

• 6x^2y + 9y^2

• 2x^2 + 3y

• 4x^2 + 9y^2

What is the first term in the trinomial factor?

• 9y^2

• 6x^2y

• 2x^2

• 4x^4

What is the final form of the factored expression?

• 8(2x^2 + 3y)(4x^4 - 6x^2y + 9y^2)

• 8(2x^2 + 3y)(4x^4 + 6x^2y + 9y^2)

• 8(2x + 3y)(4x^2 - 6xy + 9y^2)

• 8(2x^2 + 3y)(4x^2 + 6xy + 9y^2)