" 22."x^(2)+y^(2)-z^(2)-2xy

If x^(2) + y^(2) + z^(2) - xy- yz - zx = 0 , prove that : x= y = z

Factorize: 2xy-(x^(2)+y^(2)-z^(2))

Simplify: (x+y-2z)^(2)-x^(2)-y^(2)-3z^(2)+4xy

Find the following produts: (i) (x+y+2z)(x^(2)+y^(2)+4z^(2)-xy-2yz-2xz)(2x-y+2z)(4x^(2)+y^(2)+9z^(2)+2xy+3yz-6xz)

yz-x^(2)quad zx-y^(2)quad xy-z^(2)| Prove that det[[yz-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]] is divisible by (x+y+z), and hence find the quotient.

Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.

(x-y-z)^(2)-(x^(2)+y^(2)+z^(2))=2(yz-zx-xy)