Question

(y-z)³+(z-x)³+(x-y)³​

Answer 1

Step-by-step explanation:

(x-y) ³+(y-z) ³+(z-x) ³

=x^3−y^3−3xy(x−y)+y^3−z^3−3yz(y−z)+z^3−x^3−3yz(z−x)

=−3xy(x−y)−3yz(y−z)−3zx(z−x)

=-3y((x^2−xy)+yz−z^2))−3zx(z−x)

=−3y(x^2−z^2−xy+yz)−3zx(z−x)

=−3y((x−z)(x+z)−y(x−z))+3zx(x−z)

=−3(x−z)((y(x+z)−y^2)−zx)

=−3(x−z)(xy+yz−y^2−zx)

=−3(x−z)(xy−y^2−zx+yz)

=−3(x−z)(y(x−y)−z(x−y))

=−3(x−z)(x−y)(y−z)

=3(z−x)(x−y)(y−z)

Therefore value is :3(z−x)(x−y)(y−z)

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Answer 2

main concept :- A^3+B^3+C^3ABC

if A+B+C=O

given A=(X-Y)

B=(Y-X)

C=(Z-X)

their sum is A + B + C=0

so, their value is 3ABC

=3×(X-Y) (Y-Z) (Z-X)

solve it from here