Question

prove that (x-y)(x+y)+(y-z)(y+z)+(Z-x)(z+x)=0​

Answer 1

Answer:

x²+xy-xy-y²+y²+zy-zy-z²+z²+zx-zx-x²=0

0=0

Answer 2

Answer:

LHS:

(x-y)(x+y)+(y-z)(y+z)+(z-x)(z+x)

x2 - y2 + y2 - z2 + z2 - x2

x2-x2 + y2-y2 + z2-z2

0 +0 +0

0 = RHS

Hence proved..