Algebra Examples

$8 x^{4} + 8$

Step 1

Factor $8$ out of $8 x^{4} + 8$ .

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Step 1.1

Factor $8$ out of $8 x^{4}$ .

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

Step 1.2

Factor $8$ out of $8$ .

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

Step 1.3

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

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

Step 2

Multiply the constant in the polynomial $x^{4} + 1$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

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

Step 3

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

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

Step 4

Factor.

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Step 4.1

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

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

Step 4.2

Remove unnecessary parentheses.

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

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