Algebra Examples

${(x^{2} + 8)}^{2} - 36 x^{2}$

Step 1

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

${(x^{2} + 8)}^{2} - {(6 x)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2} + 8$ and $b = 6 x$ .

$(x^{2} + 8 + 6 x) (x^{2} + 8 - (6 x))$

Step 3

Simplify.

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Step 3.1

Factor $x^{2} + 8 + 6 x$ using the AC method.

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Step 3.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $6$ .

$2, 4$

Step 3.1.2

Write the factored form using these integers.

$(x + 2) (x + 4) (x^{2} + 8 - (6 x))$

Step 3.2

Multiply $6$ by $- 1$ .

$(x + 2) (x + 4) (x^{2} + 8 - 6 x)$

Step 4

Factor.

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Step 4.1

Factor $x^{2} + 8 - 6 x$ using the AC method.

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Step 4.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $- 6$ .

$- 4, - 2$

Step 4.1.2

Write the factored form using these integers.

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

Step 4.2

Remove unnecessary parentheses.

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