Precalculus Examples

x^{3} + 64

$x^{3} + 64$

Step 1

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

x^{3} + 4^{3}

$x^{3} + 4^{3}$

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 = 4

$b = 4$ .

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

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

Step 3

Simplify.

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Step 3.1

Multiply

4

$4$ by

- 1

$- 1$ .

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

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

Step 3.2

Raise

4

$4$ to the power of

2

$2$ .

(x + 4) (x^{2} - 4 x + 16)

$(x + 4) (x^{2} - 4 x + 16)$

(x + 4) (x^{2} - 4 x + 16)

$(x + 4) (x^{2} - 4 x + 16)$

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