Question

completely factor the expression, if possible.

\\8y^6 + 27\\

Explanation:

Identify the structure of the expression

Using the Factoring Sum and Difference of Cubes knowledge point

$$ 8y^6 + 27 = (2y^2)^3 + 3^3 $$

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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$$ 8y^6 + 27 = (2y^2 + 3)((2y^2)^2 - (2y^2)(3) + 3^2) $$

Simplify the factored terms

Using the Factoring Sum and Difference of Cubes knowledge point

$$ 8y^6 + 27 = (2y^2 + 3)(4y^4 - 6y^2 + 9) $$

Answer:

\((2y^2 + 3)(4y^4 - 6y^2 + 9)\)