a ) \(2x-2y-2xy+x^2+y^2\)
\(=2\left(x-y\right)+\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(x-y+2\right)\)
b ) \(\left(a^2+b^2-c^2\right)^2-4a^2b^2\)
\(=\left(a^2+b^2-c^2-2ab\right)\left(a^2+b^2-c^2+2ab\right)\)
\(=\left[\left(a^2-2ab+b^2\right)-c^2\right]\left[\left(a^2+2ab+b^2\right)-c^2\right]\)
\(=\left[\left(a-b\right)^2-c^2\right]\left[\left(a+b\right)^2-c^2\right]\)
\(=\left(a-b-c\right)\left(a-b+c\right)\left(a+b-c\right)\left(a+b+c\right)\)
\(a.2x-2y-2xy+x^2+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)\)
\(=\left(x-y\right)^2+2\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+2\right)\)
\(b.\left(a^2+b^2-c^2\right)^2-4a^2b^2=\left(a^2+b^2-c^2\right)^2-\left(2ab\right)^2\)
\(=\left(a^2+b^2-c^2+2ab\right)\left(a^2+b^2-c^2-2ab\right)\)
\(=\left[\left(a^2+2ab+b^2\right)-c^2\right]\left[\left(a^2-2ab+b^2\right)-c^2\right]\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[\left(a-b\right)^2-c^2\right]\)
\(=\left(a+b-c\right)\left(a+b+c\right)\left(a-b-c\right)\left(a-b+c\right)\)