Question

4x^2-4x+2y-y^2

Answer 1

\(4x^2-4x+2y-y^2=\left(4x^2-4x+1\right)-\left(y^2-2y+1\right)\)

\(=\left(2x-1\right)^2-\left(y-1\right)^2=\left(2x-1-y+1\right)\left(2x-1+y-1\right)\)

\(=\left(2x-y\right)\left(2x+y-2\right)\)

Answer 2

\(=\left(2x-y\right)\left(2x+y\right)-2\left(2x-y\right)=\left(2x-y\right)\left(2x+y-2\right)\)

Answer 3

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