Factor 48x^4-3y^4

$48 x^{4} - 3 y^{4}$

Step 1

Factor $3$ out of $48 x^{4} - 3 y^{4}$ .

Factor $3$ out of $48 x^{4}$ .

$3 (16 x^{4}) - 3 y^{4}$

Factor $3$ out of $- 3 y^{4}$ .

$3 (16 x^{4}) + 3 (- y^{4})$

Factor $3$ out of $3 (16 x^{4}) + 3 (- y^{4})$ .

$3 (16 x^{4} - y^{4})$

Step 2

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

$3 ({(4 x^{2})}^{2} - y^{4})$

Step 3

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

$3 ({(4 x^{2})}^{2} - {(y^{2})}^{2})$

Step 4

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

$3 ((4 x^{2} + y^{2}) (4 x^{2} - y^{2}))$

Step 5

Factor.

Simplify.

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

$3 ((4 x^{2} + y^{2}) ({(2 x)}^{2} - y^{2}))$

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 $b = y$ .

$3 ((4 x^{2} + y^{2}) ((2 x + y) (2 x - y)))$

Remove unnecessary parentheses.

$3 ((4 x^{2} + y^{2}) (2 x + y) (2 x - y))$

Remove unnecessary parentheses.

$3 (4 x^{2} + y^{2}) (2 x + y) (2 x - y)$

Factor 48x^4-3y^4

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