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

1 Answer
EZ as pi
Aug 5, 2016

#(16x^2 +9x^2)(4x+3)(4x-3)#

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:

#(16x^2 +9x^2)color(red)((16x^2-9x^2)) " difference of squares again"#

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

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