Question

completely factor the expression, if possible.

\\3y^3 + 81x^3\\

Explanation:

Factor out the greatest common factor

Using the Factoring Polynomials by GCF knowledge point

$$ 3y^3 + 81x^3 = 3(y^3 + 27x^3) $$

Rewrite the binomial as a sum of cubes

Using the Factoring Sum and Difference of Cubes knowledge point

$$ y^3 + 27x^3 = (y)^3 + (3x)^3 $$

Apply the sum of cubes formula

Using the Factoring Sum and Difference of Cubes knowledge point

$$
LATEXBLOCK0
$$

Combine the factored components

Using the Factoring Polynomials by GCF and Factoring Sum and Difference of Cubes knowledge points

$$ 3y^3 + 81x^3 = 3(y + 3x)(y^2 - 3xy + 9x^2) $$

Answer:

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