x4 + 4y4
= (x2)2 + 4x2y2 + (2y2)2 - 4x2y2
= (x2 + 2y2)2 - (2xy)2
= (x2 + 2y2 - 2xy)(x2 + 2y2 + 2xy)
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\(x^4+4y^4\)
\(=\left(x^2\right)^2+\left(2y\right)^2+4x^2y^2-4x^2y^2\)
\(=\left(x^2\right)^2+4x^2y^2+\left(2y\right)^2-4x^2y^2\)
\(=\left[\left(x^2\right)^2+4x^2y^2+\left(2y\right)^2\right]-\left(2xy\right)^2\)
\(=\left(x^2+2y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
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