Algebra Examples

n^{3} - n

$n^{3} - n$

Step 1

Factor

n

$n$ out of

n^{3} - n

$n^{3} - n$ .

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Step 1.1

Factor

n

$n$ out of

n^{3}

$n^{3}$ .

n \cdot n^{2} - n

$n \cdot n^{2} - n$

Step 1.2

Factor

n

$n$ out of

- n

$- n$ .

n \cdot n^{2} + n \cdot - 1

$n \cdot n^{2} + n \cdot - 1$

Step 1.3

Factor

n

$n$ out of

n \cdot n^{2} + n \cdot - 1

$n \cdot n^{2} + n \cdot - 1$ .

n (n^{2} - 1)

$n (n^{2} - 1)$

n (n^{2} - 1)

$n (n^{2} - 1)$

Step 2

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

n (n^{2} - 1^{2})

$n (n^{2} - 1^{2})$

Step 3

Factor.

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Step 3.1

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = n

$a = n$ and

b = 1

$b = 1$ .

n ((n + 1) (n - 1))

$n ((n + 1) (n - 1))$

Step 3.2

Remove unnecessary parentheses.

n (n + 1) (n - 1)

$n (n + 1) (n - 1)$

n (n + 1) (n - 1)

$n (n + 1) (n - 1)$

n^{3} - n

$n^{3} - n$

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