Question

Evaluate using identity :
(i) x^3(y-z)^3 + y^3 (z-x) ^3 + z^3(x-y)^3

Answer 1

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If a+b+c=0

then

a³+b³+c³ = 3abc

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x^3(y-z)^3 + y^3 (z-x) ^3 + z^3(x-y)^3

=[x(y-z)]³+[y(z-x)]³+[z(x-y)]³

Here,

a=x(y-z), b = y(z-x),c=z(x-y)

Now,

a+b+c

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

=xy-xz+yz-xy+xz-yz

=0

[x(y-z)]³+[y(z-x)]³+[z(x-y)]³

3[x(y-z)][y(z-x)][z(x-y)]

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