Factor 2x^4-54x

$2 x^{4} - 54 x$

Step 1

Factor $2 x$ out of $2 x^{4} - 54 x$ .

Factor $2 x$ out of $2 x^{4}$ .

$2 x (x^{3}) - 54 x$

Factor $2 x$ out of $- 54 x$ .

$2 x (x^{3}) + 2 x (- 27)$

Factor $2 x$ out of $2 x (x^{3}) + 2 x (- 27)$ .

$2 x (x^{3} - 27)$

Step 2

Rewrite $27$ as $3^{3}$ .

$2 x (x^{3} - 3^{3})$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 3$ .

$2 x ((x - 3) (x^{2} + x \cdot 3 + 3^{2}))$

Step 4

Factor.

Simplify.

Move $3$ to the left of $x$ .

$2 x ((x - 3) (x^{2} + 3 x + 3^{2}))$

Raise $3$ to the power of $2$ .

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

Remove unnecessary parentheses.

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

Factor 2x^4-54x

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