Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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 $b = 7$ .

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

Step 1.3

Simplify.

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Step 1.3.1

Multiply $7$ by $- 1$ .

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

Step 1.3.2

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

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

Step 2

Cancel the common factor of $x + 7$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

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

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