4 x^4+y^4 =4 x^4+4 x^2+y^4-4 x^2 y^2 = [ (2 x^2 )^2+2 x 2 x^2 x y+ (y^2 )^2 ]-(2 x y)^2 = (2 x^2+y^2 )^2-(2 x y)^2 = [ (2 x^2+y )-2 x y ] [2 (2 x+y^2 )+2 x y ] = (2 x^2-2 x y+y 2 ) (2 x^2+2 x y+y^2 )

Solve: 4 x^4+y^4

Question

Solve:
$ 4 x^4+y^4 $

✓

Answer

$ 4 x^4+y^4 $
$ =4 x^4+4 x^2+y^4-4 x^2 y^2 $
$ =\left[\left(2 x^2\right)^2+2 x 2 x^2 x y+\left(y^2\right)^2\right]-(2 x y)^2 $
$ =\left(2 x^2+y^2\right)^2-(2 x y)^2 $
$ =\left[\left(2 x^2+y\right)-2 x y\right]\left[2\left(2 x+y^2\right)+2 x y\right] $
$ =\left(2 x^2-2 x y+y 2\right)\left(2 x^2+2 x y+y^2\right) $

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