Q20 of 32 Page 2

Without actually calculating the cubes, find the value of

(–12)3 + (7)3 + (5)3.

Concept Used:


If (a + b + c) = 0, a3 + b3 + c3 = 3abc


Explanation:


Given: (–12)3 + (7)3 + (5)3


Let a = –12


b = 7


c = 5


a + b + c = –12 + 7 + 5 = 0


Therefore,


(–12)3 + (7)3 + (5)3 = 3(–12)(7)(5)


(–12)3 + (7)3 + (5)3 = –1260.


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