Waited

Calculate the value of the follow expression:

[ ( x + y + z ) 3 x 3 y 3 z 3 ] [ ( x + y + z ) 3 ( x + y z ) 3 ( y + z x ) 3 ( z + x y ) 3 ] ( x y + z x ) ( y z + x y ) ( z x + y z ) \large \frac{[(x+ y + z)^3 - x^3 - y^3 - z^3][(x + y + z)^3 - (x + y - z)^3 - (y + z - x)^3 - (z + x - y)^3]}{(xy + zx)(yz + xy)(zx + yz)}


Notation:

{ x y + z x 0 y z + x y 0 z x + y z 0 \large \left\{ \begin{aligned} xy + zx &\ne 0\\ yz + xy &\ne 0\\ zx + yz &\ne 0 \end{aligned} \right.

This is part of the series: " It's easy, believe me! "


The answer is 72.

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1 solution

Aaghaz Mahajan
Feb 26, 2018

For a shortcut, simply put a=b=c=1......and you are done!!

Seriously?

Thành Đạt Lê - 3 years, 3 months ago

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XD!!! Well....I'm trying to solve it right now using some factorization.......but its too tedious.....my method is better in competitive exams......

Aaghaz Mahajan - 3 years, 3 months ago

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