Question

plz answer this
factorize the expression:
(x-y)²(y-2z+x)+(y-z)²(z-2x+y)+(z-x)²(x-2y+z)
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Answer 1

Answer:

2x³ + 2z³ +2y³-3x²y -3y²x -3x²z -3z²x -3y²z -3z²y +12xyz

Solution:

(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)(x-2y+z)

= 2x³ + 2z³ + 2y³ -3x²y -3y²x -3x²z -3z²x -3y²z -3z²y +12xyz

[Note: For this kind of sum we first need to simplify the formula portion and then follow normal multiplication to calculate the answer]

Answer 2

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