Factor 16x^4-y^4

$16 x^{4} - y^{4}$

Step 1

Rewrite $16 x^{4}$ as ${(4 x^{2})}^{2}$ .

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

Step 2

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

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x^{2}$ and $b = y^{2}$ .

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

Step 4

Simplify.

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

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

Factor.

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

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

Remove unnecessary parentheses.

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

Factor 16x^4-y^4

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