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Question

Factor the sum or difference of cubes. Factor out the GCF first.$2 x ^ { 6 } + 54 x ^ { 3 }$

Solution

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Here we have;

\begin{aligned} &2x^6+54x^3&&\color{#19804f}\text{factor out 2x^3}\\ &=2x^3(x^3+27)&&\color{#19804f}\text{we can rewrite this as;}\\ &=2x^3(x^3+(3)^3)&&\color{#19804f}\text{factor by applying a^3+b^3=(a+b)(a^2-ab+b^2)}\\ &=\color{#c34632}2x^3(x+3)(x^2-3x+9) \end{aligned}

Therefore, we now have $\color{#c34632}\boxed{2x^3(x+3)(x^2-3x+9)}$

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