Examples

x^{3} - 8

$x^{3} - 8$

Step 1

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

x^{3} - 2^{3}

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

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})

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where

a = x

$a = x$ and

b = 2

$b = 2$ .

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

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

Step 3

Simplify.

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Step 3.1

Move

2

$2$ to the left of

x

$x$ .

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

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

Step 3.2

Raise

2

$2$ to the power of

2

$2$ .

(x - 2) (x^{2} + 2 x + 4)

$(x - 2) (x^{2} + 2 x + 4)$

(x - 2) (x^{2} + 2 x + 4)

$(x - 2) (x^{2} + 2 x + 4)$

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