Question

2) Without actually calculating the cubes, find the value of (-24)3 + (18)3 + (6)3.
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Answer 1

Answer: -7776

Step-by-step explanation:

a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)

a+b+c = -24+18+6

a+b+c = 0

So,

a^3+b^3+c^3-3abc = 0

a^3+b^3+c^3 = 3abc

3abc = 3(-24)(18)(6)

3abc = -7776