a) `(x+y)^2 +(x-y)^2`
`=(x^2 +2xy+y^2)+(x^2 -2xy+y^2)`
`=x^2 +2xy+y^2 +x^2 -2xy+y^2`
`=2x^2 +2y^2`
b) `2(x-y)(x+y)+(x+y)^2 +(x-y)^2`
`=(2x-2y)(x+y)+(x^2 +2xy+y^2)+[x^2 +(-y)+(-y)^2]`
`=(x+y+x-y)^2`
`=2x^2`
`=4x^2`
c) `(x-y+z)^2 +(z-y)^2 +2(x-y+z)(y-z)`
`=(x-y+z)^2 +2(x-y+z)(y-z)+(y-z)^2`
`=(x-y+z+y-z)^2`
`=x^2`