Algebra Examples

$(x^{2} - 2) \cdot 2 + 2 (x^{2} - 2) - 8$

Step 1

Add $(x^{2} - 2) \cdot 2$ and $2 (x^{2} - 2)$ .

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Step 1.1

Reorder $x^{2} - 2$ and $2$ .

$2 \cdot (x^{2} - 2) + 2 (x^{2} - 2) - 8$

Step 1.2

Add $2 \cdot (x^{2} - 2)$ and $2 (x^{2} - 2)$ .

$4 \cdot (x^{2} - 2) - 8$

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

Step 2

Factor $4$ out of $4 \cdot (x^{2} - 2) - 8$ .

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Step 2.1

Factor $4$ out of $- 8$ .

$4 (x^{2} - 2) + 4 \cdot - 2$

Step 2.2

Factor $4$ out of $4 (x^{2} - 2) + 4 \cdot - 2$ .

$4 (x^{2} - 2 - 2)$

Step 3

Subtract $2$ from $- 2$ .

$4 (x^{2} - 4)$

Step 4

Rewrite $4$ as $2^{2}$ .

$4 (x^{2} - 2^{2})$

Step 5

Factor.

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Step 5.1

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 $b = 2$ .

$4 ((x + 2) (x - 2))$

Step 5.2

Remove unnecessary parentheses.

$4 (x + 2) (x - 2)$