Factor x^4y-4x^2y-5y

$x^{4} y - 4 x^{2} y - 5 y$

Step 1

Factor $y$ out of $x^{4} y - 4 x^{2} y - 5 y$ .

Factor $y$ out of $x^{4} y$ .

$y x^{4} - 4 x^{2} y - 5 y$

Factor $y$ out of $- 4 x^{2} y$ .

$y x^{4} + y (- 4 x^{2}) - 5 y$

Factor $y$ out of $- 5 y$ .

$y x^{4} + y (- 4 x^{2}) + y \cdot - 5$

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

$y (x^{4} - 4 x^{2}) + y \cdot - 5$

Factor $y$ out of $y (x^{4} - 4 x^{2}) + y \cdot - 5$ .

$y (x^{4} - 4 x^{2} - 5)$

Step 2

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

$y ({(x^{2})}^{2} - 4 x^{2} - 5)$

Step 3

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

$y (u^{2} - 4 u - 5)$

Step 4

Factor $u^{2} - 4 u - 5$ using the AC method.

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 $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Write the factored form using these integers.

$y ((u - 5) (u + 1))$

Step 5

Factor.

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

$y ((x^{2} - 5) (x^{2} + 1))$

Remove unnecessary parentheses.

$y (x^{2} - 5) (x^{2} + 1)$

Factor x^4y-4x^2y-5y

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