Divide (x^3-1000)/(x-10)

$\frac{x^{3} - 1000}{x - 10}$

Step 1

Simplify the numerator.

Rewrite $1000$ as $10^{3}$ .

$\frac{x^{3} - 10^{3}}{x - 10}$

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 $b = 10$ .

$\frac{(x - 10) (x^{2} + x \cdot 10 + 10^{2})}{x - 10}$

Simplify.

Move $10$ to the left of $x$ .

$\frac{(x - 10) (x^{2} + 10 \cdot x + 10^{2})}{x - 10}$

Raise $10$ to the power of $2$ .

$\frac{(x - 10) (x^{2} + 10 x + 100)}{x - 10}$

Step 2

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{(x - 10) (x^{2} + 10 x + 100)}{x - 10}$

Divide $x^{2} + 10 x + 100$ by $1$ .

$x^{2} + 10 x + 100$

Divide (x^3-1000)/(x-10)

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