Question

Question was provided via image upload.

Explanation:

Identify the expression structure

Using the Factoring Sum and Difference of Cubes knowledge point

$$ v^6 + 27 = (v^2)^3 + 3^3 $$

Apply the sum of cubes formula

Using the Factoring Sum and Difference of Cubes knowledge point

$$ A^3 + B^3 = (A + B)(A^2 - AB + B^2) $$

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$$ v^6 + 27 = (v^2 + 3)((v^2)^2 - (v^2)(3) + 3^2) $$

Simplify the factored terms

Using the Factoring Sum and Difference of Cubes knowledge point

$$ v^6 + 27 = (v^2 + 3)(v^4 - 3v^2 + 9) $$

Answer:

Completely factor the expression, if possible.
\(v^6 + 27 =\) <blank>\((v^2 + 3)(v^4 - 3v^2 + 9)\)</blank>