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Question:

Without actually calculating the cubes, find the value of each of the following:
(i)(-4)³ + (7)³ + (5)³
(ii)(28)³ + (-17)³ + (-15)³

Solution:

(i)(-4)³ + (7)³ + (5)³ = (-4 + 7 + 5)³ + 3(-4)(7)(5) = 0³ + 3(-140) = 0 + (-420) = -420
(ii)(28)³ + (-17)³ + (-15)³ = (28 - 17 - 15)³ + 3(28)(-17)(-15) = 0³ + 21420 = 21420