" 12."x^(2)+y^(2)+2(xy-yz=2x)

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

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)

If x=997 , y=998 z=999 then the value of x^(2)+y^(2)+z^(2)-xy-yz-zx will be

Factorise : 4x^(2) + 9y^(2) + z^(2) + 12xy - 6yz - 4zx

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.

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.

Factorise the following expression: ( i) 4x^(2) +9y^(2) +25z^(2) +12xy +30yz + 20zx (ii) 25x^(2) +4y^(2) +9z^(2) -20 xy +12yz - 30zx

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

If x+y+z =10 , x^(2) +y^(2) +z^(2) =60 then value of xy+yz +zx is