Trigonometry Examples

$x^{2} y^{2} - 4 x y - 12$

Step 1

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

${(x y)}^{2} - 4 (x y) - 12$

Step 2

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$u^{2} - 4 u - 12$

Step 3

Factor $u^{2} - 4 u - 12$ 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 $- 12$ and whose sum is $- 4$ .

$- 6, 2$

Step 3.2

Write the factored form using these integers.

$(u - 6) (u + 2)$

Step 4

Replace all occurrences of $u$ with $x y$ .

$(x y - 6) (x y + 2)$