Simplify (x^3+125)/(x+5)

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

Step 1

Simplify the numerator.

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

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

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

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

Simplify.

Multiply $5$ by $- 1$ .

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

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

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

Step 2

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

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

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

Simplify (x^3+125)/(x+5)

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