Factoring Difference of Cubes

The video tutorial explains how to factor the expression 8X^3 - 27y^3 using the difference of cubes formula. It begins by introducing the formula and then demonstrates how to transform the terms 8X^3 and 27y^3 into forms that fit the formula. The tutorial concludes with the final calculation, resulting in the factored form of the expression.

What is the initial expression that needs to be factored?

• 8X cubed minus 27y cubed

• 8X squared plus 27y squared

• 8X squared minus 27y squared

• 8X cubed plus 27y cubed

Which formula is used to factor the expression?

• Difference of cubes

• Sum of cubes

• Difference of squares

• Sum of squares

In the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2), what does 'a' represent in the expression 8X cubed?

• 2x

• 8x

• 3y

• 27y

In the expression 27y cubed, what does 'b' represent?

• 27y

• 2x

• 3y

• 8x

What is the first step in applying the difference of cubes formula to the expression?

• Subtract the terms

• Identify a and b

• Multiply the terms

• Add the terms

What is the cube root of 8X cubed?

• 2x

• 3x

• 4x

• 8x

What is the cube root of 27y cubed?

• 9y

• 6y

• 3y

• 27y

What is the result of squaring 2x in the expression?

• 8x^2

• 2x

• 16x^2

• 4x^2

What is the final factored form of the expression?

• (2x + 3y)(4x^2 - 6xy + 9y^2)

• (2x - 3y)(4x^2 + 6xy + 9y^2)

• (2x + 3y)(4x^2 + 6xy + 9y^2)

• (2x - 3y)(4x^2 - 6xy + 9y^2)

What operation is performed between a and b in the middle term of the formula a^2 + ab + b^2?

• Division

• Addition

• Subtraction

• Multiplication