Question

factor.
$27y^3 + 125$

Explanation:

Step1: Identify the sum of cubes

Recognize that \(27y^3=(3y)^3\) and \(125 = 5^3\). So the expression \(27y^3 + 125\) is a sum of cubes, which follows the formula \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(a = 3y\) and \(b = 5\).

Step2: Apply the sum of cubes formula

Substitute \(a = 3y\) and \(b = 5\) into the formula:

$$
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Answer:

\((3y + 5)(9y^2 - 15y + 25)\)