Algebra Examples

x^{3} - 125

$x^{3} - 125$

Step 1

Rewrite

125

$125$ as

5^{3}

$5^{3}$ .

x^{3} - 5^{3}

$x^{3} - 5^{3}$

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 = 5

$b = 5$ .

(x - 5) (x^{2} + x \cdot 5 + 5^{2})

$(x - 5) (x^{2} + x \cdot 5 + 5^{2})$

Step 3

Simplify.

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Step 3.1

Move

5

$5$ to the left of

x

$x$ .

(x - 5) (x^{2} + 5 x + 5^{2})

$(x - 5) (x^{2} + 5 x + 5^{2})$

Step 3.2

Raise

5

$5$ to the power of

2

$2$ .

(x - 5) (x^{2} + 5 x + 25)

$(x - 5) (x^{2} + 5 x + 25)$

(x - 5) (x^{2} + 5 x + 25)

$(x - 5) (x^{2} + 5 x + 25)$