# How do you factor 768x^4-3y^4?

Apr 28, 2016

$3 \left(4 x - y\right) \left(4 x + y\right) \left(16 {x}^{2} + {y}^{2}\right)$

#### Explanation:

Algebraic identity:

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

Factorise out the common factors in $768 {x}^{4} - 3 {y}^{4}$.

$768 {x}^{4} - 3 {y}^{4} = 3 \left(256 {x}^{4} - {y}^{4}\right)$

You can write

$256 {x}^{4} - {y}^{4} = {\left(16 {x}^{2}\right)}^{2} - {\left({y}^{2}\right)}^{2} = \left(16 {x}^{2} - {y}^{2}\right) \left(16 {x}^{2} + {y}^{2}\right)$

You can write

$16 {x}^{2} - {y}^{2} = {\left(4 x\right)}^{2} - {y}^{2} = \left(4 x - y\right) \left(4 x + y\right)$

Put this back together to get

$768 {x}^{4} - 3 {y}^{4} = 3 \left(4 x - y\right) \left(4 x + y\right) \left(16 {x}^{2} + {y}^{2}\right)$