Algebra Examples

$(1 + a^{3}) \div (1 + a)$

Step 1

Rewrite the division as a fraction.

$\frac{1 + a^{3}}{1 + a}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{3}$ .

$\frac{1^{3} + a^{3}}{1 + a}$

Step 2.2

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 $a = 1$ and $b = a$ .

$\frac{(1 + a) (1^{2} - 1 a + a^{2})}{1 + a}$

Step 2.3

Simplify.

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Step 2.3.1

One to any power is one.

$\frac{(1 + a) (1 - 1 a + a^{2})}{1 + a}$

Step 2.3.2

Rewrite $- 1 a$ as $- a$ .

$\frac{(1 + a) (1 - a + a^{2})}{1 + a}$

Step 3

Cancel the common factor of $1 + a$ .

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Step 3.1

Cancel the common factor.

$\frac{(1 + a) (1 - a + a^{2})}{1 + a}$

Step 3.2

Divide $1 - a + a^{2}$ by $1$ .

$1 - a + a^{2}$