Algebra Examples

$\frac{d^{3} - a^{3}}{d^{2} - a^{2}}$

Step 1

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 $a = d$ and $b = a$ .

$\frac{(d - a) (d^{2} + d a + a^{2})}{d^{2} - a^{2}}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = d$ and $b = a$ .

$\frac{(d - a) (d^{2} + d a + a^{2})}{(d + a) (d - a)}$

Step 3

Cancel the common factor of $d - a$ .

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Step 3.1

Cancel the common factor.

$\frac{(d - a) (d^{2} + d a + a^{2})}{(d + a) (d - a)}$

Step 3.2

Rewrite the expression.

$\frac{d^{2} + d a + a^{2}}{d + a}$