Divide (x^3-343)/(x-7)

$\frac{x^{3} - 343}{x - 7}$

Step 1

Simplify the numerator.

Rewrite $343$ as $7^{3}$ .

$\frac{x^{3} - 7^{3}}{x - 7}$

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 $b = 7$ .

$\frac{(x - 7) (x^{2} + x \cdot 7 + 7^{2})}{x - 7}$

Simplify.

Move $7$ to the left of $x$ .

$\frac{(x - 7) (x^{2} + 7 \cdot x + 7^{2})}{x - 7}$

Raise $7$ to the power of $2$ .

$\frac{(x - 7) (x^{2} + 7 x + 49)}{x - 7}$

Step 2

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{(x - 7) (x^{2} + 7 x + 49)}{x - 7}$

Divide $x^{2} + 7 x + 49$ by $1$ .

$x^{2} + 7 x + 49$

Divide (x^3-343)/(x-7)

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