Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\\y^3 + 27\\

Explanation:

Identify the structure of the expression

Using the Factoring Sum and Difference of Cubes knowledge point

$$ y^3 + 27 = y^3 + 3^3 $$

Apply the sum of cubes formula

Using the Factoring Sum and Difference of Cubes knowledge point

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

$$ y^3 + 3^3 = (y + 3)(y^2 - 3y + 3^2) = (y + 3)(y^2 - 3y + 9) $$

Answer:

Completely factor the given polynomial, if possible. If the polynomial cannot be factored, indicate "Not Factorable".

\(y^3 + 27 =\) <blank>\((y + 3)(y^2 - 3y + 9)\)</blank>