Question

Without actually calculating the cubes, find the value of each of the following:
(i) $(-12{)}^3+(7{)}^3+(5{)}^3$
(ii) $(28{)}^3+(-15{)}^3+(-13{)}^3$

Answer 1

(i) $(-12{)}^3+(7{)}^3+(5{)}^3=(-12+7+5)+3(-12\left)\right(7\left)\right(5)=0+1260=1260$

(ii) $(28{)}^3+(-15{)}^3+(-13{)}^3=(28-15-13)+3(28\left)\right(-15\left)\right(-13)=0+16380=16380$