Question

(x-y+x)² + (z-y)² + 2(x-y+z)(y+z)

Answer 1

Ta có: (x-y+x)² + (z-y)² + 2(x-y+z)(y+z)

= x²+y²+x²-2xy-2xy+2x²+z²-2zy+y²+2xy+2xz-2y²-2yz+2yz+2z²

= 4x²-2xy+2xz+3z²

Answer 2

\(\left(x-y+x\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y+z\right)\)

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

\(=4x^2-4xy+y^2+z^2-2zy+y^2+2xy-2y^2+2yz+2xz-2yz+2z^2\)

\(=4x^2+\left(y^2+y^2-2y^2\right)+\left(z^2+2z^2\right)+\left(-4xy+2xy\right)+\left(2yz-2yz-2yz\right)+2xz\)

\(=4x^2+3z^2-2xy-2yz+2xz\)