Question

Simplify the following expressions:

${\displaystyle {(x+y-2z)}^2-x^2-y^2-3z^2+4xy}$

Answer 1

We have,

${\displaystyle {(x+y-2z)}^2-x^2-y^2-3z^2+4xy}$

${\displaystyle =[x^2+y^2+{(-2z)}^2+ 2xy+2\left(y\right)(-2z)]-x^2 -y^2-3z^2+4xy}$

${\displaystyle =x^2+y^2+4z^2+2xy-4yz-x^2-y^2-3z^2=4xy}$

${\displaystyle =z^2+6xy-4yz-4zx}$

${\displaystyle \therefore {(x+y-2z)}^2-x^2-y^2-3z^2+4xy=z^2+6xy-4yz-4zx}$