Pre-Algebra Examples

$2 x - 54 x^{4}$

Step 1

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

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Step 1.1

Factor $2 x$ out of $2 x$ .

$2 x (1) - 54 x^{4}$

Step 1.2

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

$2 x (1) + 2 x (- 27 x^{3})$

Step 1.3

Factor $2 x$ out of $2 x (1) + 2 x (- 27 x^{3})$ .

$2 x (1 - 27 x^{3})$

Step 2

Rewrite $1$ as $1^{3}$ .

$2 x (1^{3} - 27 x^{3})$

Step 3

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$2 x (1^{3} - {(3 x)}^{3})$

Step 4

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 $a = 1$ and $b = 3 x$ .

$2 x ((1 - (3 x)) (1^{2} + 1 (3 x) + {(3 x)}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Multiply $3$ by $- 1$ .

$2 x ((1 - 3 x) (1^{2} + 1 (3 x) + {(3 x)}^{2}))$

Step 5.1.2

One to any power is one.

$2 x ((1 - 3 x) (1 + 1 (3 x) + {(3 x)}^{2}))$

Step 5.1.3

Multiply $3 x$ by $1$ .

$2 x ((1 - 3 x) (1 + 3 x + {(3 x)}^{2}))$

Step 5.1.4

Apply the product rule to $3 x$ .

$2 x ((1 - 3 x) (1 + 3 x + 3^{2} x^{2}))$

Step 5.1.5

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

$2 x ((1 - 3 x) (1 + 3 x + 9 x^{2}))$

Step 5.2

Remove unnecessary parentheses.

$2 x (1 - 3 x) (1 + 3 x + 9 x^{2})$