Question

completely factor the expression, if possible.

\\27y^3 - 64x^3\\

Explanation:

Identify the structure of the expression

Using the Difference of Cubes knowledge point

$$ 27y^3 - 64x^3 = (3y)^3 - (4x)^3 $$

Apply the factoring formula

Using the Factoring Sum and Difference of Cubes knowledge point

$$ a^3 - b^3 = (a - b)(a^2 + ab + b^2) $$

$$
LATEXBLOCK0
$$

$$ 27y^3 - 64x^3 = (3y - 4x)((3y)^2 + (3y)(4x) + (4x)^2) $$

Simplify the terms

Using the Factoring Sum and Difference of Cubes knowledge point

$$ 27y^3 - 64x^3 = (3y - 4x)(9y^2 + 12xy + 16x^2) $$

Answer:

\((3y - 4x)(9y^2 + 12xy + 16x^2)\)