Algebra Examples

$\frac{x^{3} - 125}{x - 5}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $125$ as $5^{3}$ .

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

Step 1.2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 5$ .

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

Step 1.3

Simplify.

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Step 1.3.1

Move $5$ to the left of $x$ .

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

Step 1.3.2

Raise $5$ to the power of $2$ .

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

Step 2

Cancel the common factor of $x - 5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $x^{2} + 5 x + 25$ by $1$ .

$x^{2} + 5 x + 25$