Question
Solve:
$4 x^4+y^4$
$4 x^4+y^4$
✓
Answer
$4 x^4+y^4$
$= 4 x^4+4 x^2+y^4-4 x^2 y^2$
$= {\left[\left(2 x^2\right)^2+2 x 2 x^2 x y+\left(y^2\right)^2\right]-(2 x y)^2 }$
$= \left(2 x^2+y^2\right)^2-(2 x y)^2$
$= {\left[\left(2 x^2+y\right)-2 x y\right]\left[2\left(2 x+y^2\right)+2 x y\right] }$
$= \left(2 x^2-2 x y+y 2\right)\left(2 x^2+2 x y+y^2\right)$
$= 4 x^4+4 x^2+y^4-4 x^2 y^2$
$= {\left[\left(2 x^2\right)^2+2 x 2 x^2 x y+\left(y^2\right)^2\right]-(2 x y)^2 }$
$= \left(2 x^2+y^2\right)^2-(2 x y)^2$
$= {\left[\left(2 x^2+y\right)-2 x y\right]\left[2\left(2 x+y^2\right)+2 x y\right] }$
$= \left(2 x^2-2 x y+y 2\right)\left(2 x^2+2 x y+y^2\right)$
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