Quantitative Aptitude :: Simplification - Discussion

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Explanation:
take 77!=a
and 54!=b
now the given expression will look like
(a(a-2b)^3 )/(a+b)^3 + (b(2a-b)^3 )/(a+b)^3

( a (a^3 - 6a^2 b + 12ab^2 - 8b^3) + b (8a^3 - 12a^2 b + 6ab^2 - b^3) ) / (a+b)^3
(a^4 - 6a^3 b + 12 a^2 b^2 - 8ab^3 + 8a^3 b - 12a^2 b^2 + 6ab^3 - b^4) / (a+b)^3
(a^4 + 2a^3 b - 2ab^3 - b^4) / (a+b)^3
( a^4 - b^4 + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 + b^2)(a^2 - b^2) + 2ab(a^2 - b^2) ) / (a+b)^3
( (a^2 - b^2) (a^2 + b^2 + 2ab) ) / (a+b)^3
( (a^2 - b^2)(a+b)^2 ) / (a+b)^3
( (a+b)(a-b) (a+b)^2 ) / (a+b)^3
( (a+b)^3 (a-b) ) / (a+b)^3
a-b
i.e 77! - 54!