Precalculus Examples

x^{3} + 216

$x^{3} + 216$

Step 1

Rewrite

216

$216$ as

6^{3}

$6^{3}$ .

x^{3} + 6^{3}

$x^{3} + 6^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum 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 = 6

$b = 6$ .

(x + 6) (x^{2} - x \cdot 6 + 6^{2})

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

Step 3

Simplify.

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Step 3.1

Multiply

6

$6$ by

- 1

$- 1$ .

(x + 6) (x^{2} - 6 x + 6^{2})

$(x + 6) (x^{2} - 6 x + 6^{2})$

Step 3.2

Raise

6

$6$ to the power of

2

$2$ .

(x + 6) (x^{2} - 6 x + 36)

$(x + 6) (x^{2} - 6 x + 36)$

(x + 6) (x^{2} - 6 x + 36)

$(x + 6) (x^{2} - 6 x + 36)$

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