Question

factor the expression, if possible.

\\3 - 192y^3\\

Explanation:

Factor out the greatest common factor

Using the Greatest Common Factor and Factoring Polynomials by GCF knowledge points

$$ 3 - 192y^3 = 3(1 - 64y^3) $$

Identify the difference of cubes

Using the Difference of Cubes knowledge point

$$ 1 - 64y^3 = 1^3 - (4y)^3 $$

Apply the difference of cubes formula

Using the Factoring Sum and Difference of Cubes knowledge point

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

$$ 1^3 - (4y)^3 = (1 - 4y)(1^2 + 1(4y) + (4y)^2) = (1 - 4y)(1 + 4y + 16y^2) $$

Combine all factored parts

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

$$ 3 - 192y^3 = 3(1 - 4y)(1 + 4y + 16y^2) $$

Answer:

Factor the expression, if possible.

\(3 - 192y^3 =\) <blank>\(3(1 - 4y)(1 + 4y + 16y^2)\)</blank>