Basic Math Examples

$\frac{64 a^{3}}{16 a^{2} + 4 a b + b^{2}} - \frac{b^{3}}{16 a^{2} + 4 a b + b^{2}}$

Step 1

Combine the numerators over the common denominator.

$\frac{64 a^{3} - b^{3}}{16 a^{2} + 4 a b + b^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $64 a^{3}$ as ${(4 a)}^{3}$ .

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

Step 2.2

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

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

Step 2.3

Simplify.

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Step 2.3.1

Apply the product rule to $4 a$ .

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

Step 2.3.2

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

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

Step 3

Cancel the common factor of $16 a^{2} + 4 a b + b^{2}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $4 a - b$ by $1$ .

$4 a - b$