Algebra Examples

5 x^{2} - 5

$5 x^{2} - 5$

Step 1

Factor

5

$5$ out of

5 x^{2} - 5

$5 x^{2} - 5$ .

Tap for more steps...

Step 1.1

Factor

5

$5$ out of

5 x^{2}

$5 x^{2}$ .

5 (x^{2}) - 5

$5 (x^{2}) - 5$

Step 1.2

Factor

5

$5$ out of

- 5

$- 5$ .

5 (x^{2}) + 5 (- 1)

$5 (x^{2}) + 5 (- 1)$

Step 1.3

Factor

5

$5$ out of

5 (x^{2}) + 5 (- 1)

$5 (x^{2}) + 5 (- 1)$ .

5 (x^{2} - 1)

$5 (x^{2} - 1)$

5 (x^{2} - 1)

$5 (x^{2} - 1)$

Step 2

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

5 (x^{2} - 1^{2})

$5 (x^{2} - 1^{2})$

Step 3

Factor.

Tap for more steps...

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 = x

$a = x$ and

b = 1

$b = 1$ .

5 ((x + 1) (x - 1))

$5 ((x + 1) (x - 1))$

Step 3.2

Remove unnecessary parentheses.

5 (x + 1) (x - 1)

$5 (x + 1) (x - 1)$

5 (x + 1) (x - 1)

$5 (x + 1) (x - 1)$