Algebra Examples

$\frac{27 - x^{3}}{{(3 - x)}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $27$ as $3^{3}$ .

$\frac{3^{3} - x^{3}}{{(3 - x)}^{2}}$

Step 1.2

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 $a = 3$ and $b = x$ .

$\frac{(3 - x) (3^{2} + 3 x + x^{2})}{{(3 - x)}^{2}}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{(3 - x) (9 + 3 x + x^{2})}{{(3 - x)}^{2}}$

Step 2

Cancel the common factors.

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Step 2.1

Factor $3 - x$ out of ${(3 - x)}^{2}$ .

$\frac{(3 - x) (9 + 3 x + x^{2})}{(3 - x) (3 - x)}$

Step 2.2

Cancel the common factor.

$\frac{(3 - x) (9 + 3 x + x^{2})}{(3 - x) (3 - x)}$

Step 2.3

Rewrite the expression.

$\frac{9 + 3 x + x^{2}}{3 - x}$