P=(x-y)2+(x+y)2-2(x+y)(x-y)-4x2
=[(x-y)2-2(x-y)(x+y)+(x+y)2]-4x2
=[(x-y)-(x+y)]2-4x2
=(x-y-x-y)2-4x2
=(-2y)2-4x2
=(-2y-2x)(-2y+2x)
=-(2y+2x)(2x-2y)
\(P=\left(x-y\right)^2+\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)-4x^2\)
\(\Leftrightarrow P=\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2-4x^2\)
\(\Leftrightarrow P=\left(x+y-x+y\right)^2-4x^2\)
\(\Leftrightarrow P=\left(2y\right)^2-4x^2\)
\(\Leftrightarrow P=4y^2-4x^2\)