Question

factor completely using the formula for sum or difference of cubes.
$2x^3 + 54 = \square$
question help: \\(\triangleright\\) video
add work

Explanation:

Step1: Factor out the GCF

First, we find the greatest common factor (GCF) of \(2x^{3}\) and \(54\). The GCF of \(2\) and \(54\) is \(2\). So we factor out \(2\) from the expression:
\(2x^{3}+54 = 2(x^{3}+27)\)

Step2: Apply the sum of cubes formula

The sum of cubes formula is \(a^{3}+b^{3}=(a + b)(a^{2}-ab + b^{2})\). Now, we recognize that \(x^{3}+27\) can be written as \(x^{3}+3^{3}\), where \(a = x\) and \(b = 3\). Applying the sum of cubes formula:
\(x^{3}+3^{3}=(x + 3)(x^{2}-x\times3+3^{2})=(x + 3)(x^{2}-3x + 9)\)

Step3: Combine the factors

We already factored out \(2\) in Step 1, so now we combine the factors:
\(2x^{3}+54=2(x + 3)(x^{2}-3x + 9)\)

Answer:

\(2(x + 3)(x^{2}-3x + 9)\)