# How do you factor completely 256x^4-81y^4?

Aug 5, 2016

$\left(16 {x}^{2} + 9 {x}^{2}\right) \left(4 x + 3\right) \left(4 x - 3\right)$

#### Explanation:

This is the difference of squares.
Easy to do, but often tricky to recognize if you do not know the square numbers.
Clues are: there are 2 terms, with a minus sign,
the powers are even and the numbers are squares:

Hence:

$\left(16 {x}^{2} + 9 {x}^{2}\right) \textcolor{red}{\left(16 {x}^{2} - 9 {x}^{2}\right)} \text{ difference of squares again}$

=(16x^2 +9x^2)color(red)((4x+3)(4x-3)