Algebra Examples

$\frac{64 - m^{3}}{{(4 - m)}^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $64$ as $4^{3}$ .

$\frac{4^{3} - m^{3}}{{(4 - m)}^{3}}$

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 $a = 4$ and $b = m$ .

$\frac{(4 - m) (4^{2} + 4 m + m^{2})}{{(4 - m)}^{3}}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{(4 - m) (16 + 4 m + m^{2})}{{(4 - m)}^{3}}$

Step 2

Cancel the common factors.

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Step 2.1

Factor $4 - m$ out of ${(4 - m)}^{3}$ .

$\frac{(4 - m) (16 + 4 m + m^{2})}{(4 - m) {(4 - m)}^{2}}$

Step 2.2

Cancel the common factor.

$\frac{(4 - m) (16 + 4 m + m^{2})}{(4 - m) {(4 - m)}^{2}}$

Step 2.3

Rewrite the expression.

$\frac{16 + 4 m + m^{2}}{{(4 - m)}^{2}}$