Question

question
enter the correct answer in the box.
use the sum of cubes identity to write this polynomial expression in factored form:
8x³ + 27.

Explanation:

Step1: Recall sum of cubes formula

The sum of cubes identity is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Identify \(a\) and \(b\)

For \(8x^3+27\), we can rewrite \(8x^3=(2x)^3\) and \(27 = 3^3\). So \(a = 2x\) and \(b=3\).

Step3: Apply the formula

Substitute \(a = 2x\) and \(b = 3\) into the sum of cubes formula:
\((2x)^3+3^3=(2x + 3)((2x)^2-(2x)(3)+3^2)\)

Step4: Simplify the terms

Simplify \((2x)^2=4x^2\), \((2x)(3) = 6x\) and \(3^2 = 9\). So we get \((2x + 3)(4x^2-6x + 9)\).

Answer:

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