Algebra Examples

x^{3} - 27

$x^{3} - 27$

Step 1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

x^{3} - 3^{3}

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

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 = 3

$b = 3$ .

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

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

Step 3

Simplify.

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Step 3.1

Move

3

$3$ to the left of

x

$x$ .

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

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

Step 3.2

Raise

3

$3$ to the power of

2

$2$ .

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

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

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

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

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