Factor 4x^4-144y^4

$4 x^{4} - 144 y^{4}$

Step 1

Factor $4$ out of $4 x^{4} - 144 y^{4}$ .

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

$4 (x^{4}) - 144 y^{4}$

Factor $4$ out of $- 144 y^{4}$ .

$4 (x^{4}) + 4 (- 36 y^{4})$

Factor $4$ out of $4 (x^{4}) + 4 (- 36 y^{4})$ .

$4 (x^{4} - 36 y^{4})$

Step 2

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

$4 ({(x^{2})}^{2} - 36 y^{4})$

Step 3

Rewrite $36 y^{4}$ as ${(6 y^{2})}^{2}$ .

$4 ({(x^{2})}^{2} - {(6 y^{2})}^{2})$

Step 4

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

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

Step 5

Factor.

Multiply $6$ by $- 1$ .

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

Remove unnecessary parentheses.

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

Factor 4x^4-144y^4

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