(y-z)³+(z-x)³+(x-y)³
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Answered by
4
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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Answered by
0
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
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