Divide (x^3+512)/(x+8)

$\frac{x^{3} + 512}{x + 8}$

Step 1

Simplify the numerator.

Rewrite $512$ as $8^{3}$ .

$\frac{x^{3} + 8^{3}}{x + 8}$

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 $b = 8$ .

$\frac{(x + 8) (x^{2} - x \cdot 8 + 8^{2})}{x + 8}$

Simplify.

Multiply $8$ by $- 1$ .

$\frac{(x + 8) (x^{2} - 8 x + 8^{2})}{x + 8}$

Raise $8$ to the power of $2$ .

$\frac{(x + 8) (x^{2} - 8 x + 64)}{x + 8}$

Step 2

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{(x + 8) (x^{2} - 8 x + 64)}{x + 8}$

Divide $x^{2} - 8 x + 64$ by $1$ .

$x^{2} - 8 x + 64$

Divide (x^3+512)/(x+8)

Related Questions

Support LCMGCF.com by disabling your adblocker.