Algebra Examples

$a^{4} - 2 a^{2} - 15$

Step 1

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

${(a^{2})}^{2} - 2 a^{2} - 15$

Step 2

Let $u = a^{2}$ . Substitute $u$ for all occurrences of $a^{2}$ .

$u^{2} - 2 u - 15$

Step 3

Factor $u^{2} - 2 u - 15$ using the AC method.

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Step 3.1

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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Step 3.2

Write the factored form using these integers.

$(u - 5) (u + 3)$

Step 4

Replace all occurrences of $u$ with $a^{2}$ .

$(a^{2} - 5) (a^{2} + 3)$