Algebra Examples

$x^{4} + 2 x^{2} + 9$

Step 1

Rewrite the middle term.

$x^{4} + 2 x^{2} \cdot 3 - 4 x^{2} + 9$

Step 2

Rearrange terms.

$x^{4} + 2 x^{2} \cdot 3 + 9 - 4 x^{2}$

Step 3

Factor first three terms by perfect square rule.

${(x^{2} + 3)}^{2} - 4 x^{2}$

Step 4

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

${(x^{2} + 3)}^{2} - {(2 x)}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2} + 3$ and $b = 2 x$ .

$(x^{2} + 3 + 2 x) (x^{2} + 3 - (2 x))$

Step 6

Simplify.

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Step 6.1

Reorder terms.

$(x^{2} + 2 x + 3) (x^{2} + 3 - (2 x))$

Step 6.2

Multiply $2$ by $- 1$ .

$(x^{2} + 2 x + 3) (x^{2} + 3 - 2 x)$

Step 6.3

Reorder terms.

$(x^{2} + 2 x + 3) (x^{2} - 2 x + 3)$