Algebra Examples

$\frac{x^{4} - 1}{x - 1}$

Step 1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{{(x^{2})}^{2} - 1}{x - 1}$

Step 2

Rewrite $1$ as $1^{2}$ .

$\frac{{(x^{2})}^{2} - 1^{2}}{x - 1}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 1$ .

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

Step 4

Simplify.

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Step 4.1

Rewrite $1$ as $1^{2}$ .

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

Step 4.2

Factor.

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Step 4.2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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

Step 4.2.2

Remove unnecessary parentheses.

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

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Reduce the expression $\frac{(x^{2} + 1) (x + 1) (x - 1)}{x - 1}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

$\frac{(x^{2} + 1) (x + 1)}{1}$

Step 5.2

Divide $(x^{2} + 1) (x + 1)$ by $1$ .

$(x^{2} + 1) (x + 1)$