Precalculus Examples

$x^{3} - 3 x + 3 x - 1$

Step 1

Add $- 3 x$ and $3 x$ .

$x^{3} + 0 - 1$

Step 2

Add $x^{3}$ and $0$ .

$x^{3} - 1$

Step 3

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

$x^{3} - 1^{3}$

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

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

Step 5

Simplify.

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Step 5.1

Multiply $x$ by $1$ .

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

Step 5.2

One to any power is one.

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