Question

Hey plz answer this
Factorize the expression:
(x-y)²(y-2z+x)+(y-z)²(z-2x+y)+(z-x)²(x-2y+z)​

Answer 1

Ans:- (x-y)²(y-2z+x)+(y-z)²(z-2x+y)+(z-x)²(x-2y+z)

= (x²-2xy+y²)(y-2z+x) + (y²-2yz+z²)(z-2x+y) + (z²-2zx+x²)(z-2x+y)

= yx²-2zx²+x³-2xy²+4xyz-2yx²+y³-2zy²+xy² + zy²-2xy²+y³-2yz²+4xyz-2zy²+z³-2xz²+yz² + z³-2xz²+yz²-2xz²+4zx²-2xyz+zx²-2x³+yx²

= x³-2x³+y³+y³+z³+z³+3zx²-3xy²-3zy²-6xz²+6xyz

= -x³+2y³+2z³-3xy²-3zy²+3zx²-6xz²+6xyz

= (-x+2y+2z)³

= (-x+2y+2z)(-x+2y+2z)(-x+2y+2z)

here is your answer

hope it will help you