Pre-Algebra Examples

$\frac{x^{6} + 4 x^{4} - 4 x - 1}{x^{3} - 1}$

Step 1

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

$\frac{x^{6} + 4 x^{4} - 4 x - 1}{x^{3} - 1^{3}}$

Step 2

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 $b = 1$ .

$\frac{x^{6} + 4 x^{4} - 4 x - 1}{(x - 1) (x^{2} + x \cdot 1 + 1^{2})}$

Step 3

Simplify.

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Step 3.1

Multiply $x$ by $1$ .

$\frac{x^{6} + 4 x^{4} - 4 x - 1}{(x - 1) (x^{2} + x + 1^{2})}$

Step 3.2

One to any power is one.

$\frac{x^{6} + 4 x^{4} - 4 x - 1}{(x - 1) (x^{2} + x + 1)}$