Algebra Examples

8 x^{4} + 8

$8 x^{4} + 8$

Step 1

Factor

8

$8$ out of

8 x^{4} + 8

$8 x^{4} + 8$ .

Tap for more steps...

Step 1.1

Factor

8

$8$ out of

8 x^{4}

$8 x^{4}$ .

8 (x^{4}) + 8

$8 (x^{4}) + 8$

Step 1.2

Factor

8

$8$ out of

8

$8$ .

8 (x^{4}) + 8 (1)

$8 (x^{4}) + 8 (1)$

Step 1.3

Factor

8

$8$ out of

8 (x^{4}) + 8 (1)

$8 (x^{4}) + 8 (1)$ .

8 (x^{4} + 1)

$8 (x^{4} + 1)$

8 (x^{4} + 1)

$8 (x^{4} + 1)$

Step 2

Multiply the constant in the polynomial

x^{4} + 1

$x^{4} + 1$ by

- i^{2}

$- i^{2}$ where

i^{2}

$i^{2}$ is equal to

- 1

$- 1$ .

8 (x^{4} - 1 i^{2})

$8 (x^{4} - 1 i^{2})$

Step 3

Rewrite

x^{4}

$x^{4}$ as

{(x^{2})}^{2}

${(x^{2})}^{2}$ .

8 ({(x^{2})}^{2} - 1 i^{2})

$8 ({(x^{2})}^{2} - 1 i^{2})$

Step 4

Factor.

Tap for more steps...

Step 4.1

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

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

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

a = x^{2}

$a = x^{2}$ and

i = i

$i = i$ .

8 ((x^{2} + i) (x^{2} - i))

$8 ((x^{2} + i) (x^{2} - i))$

Step 4.2

Remove unnecessary parentheses.

8 (x^{2} + i) (x^{2} - i)

$8 (x^{2} + i) (x^{2} - i)$

8 (x^{2} + i) (x^{2} - i)

$8 (x^{2} + i) (x^{2} - i)$

Enter YOUR Problem