Question

find the value of (x-y)³ + (y-z) ³ + (z-x)³​

Answer 1

Answer:

(x-y) ³+(y-z) ³+(z-x) ³

= x3−y3−3xy(x−y)+y3−z3−3yz(y−z)+z3−x3−3yz(z−x)  

= −3xy(x−y)−3yz(y−z)−3zx(z−x)  

=- 3y((x2−xy)+yz−z2))−3zx(z−x)  

= −3y(x2−z2−xy+yz)−3zx(z−x)  

= −3y((x−z)(x+z)−y(x−z))+3zx(x−z)  

= −3(x−z)((y(x+z)−y2)−zx)  

= −3(x−z)(xy+yz−y2−zx)  

= −3(x−z)(xy−y2−z x +yz)  

= −3(x−z)(y(x−y)−z(x−y))  

= −3(x−z)(x−y)(y−z)  

= 3(z−x)(x−y)(y−z)  

Ans: 3(z−x)(x−y)(y−z)