Question

${111}^3-{89}^3$.

Answer 1

The given expression ${111}^3-{89}^3$ can be rewritten as $(100+11{)}^3-(100-11{)}^3$ and we solve it as follows:

$(100+11{)}^3-(100-11{)}^3=[{100}^3+{11}^3+(3\times {100}^2\times 11)+(3\times 100\times {11}^2\left)\right]-[{100}^3-{11}^3-(3\times {100}^2\times 11)+(3\times 100\times {11}^2\left)\right](\because (x+y{)}^3=x^3+y^3+3x^{2}y+3x{y}^2,(x-y{)}^3=x^3-y^3-3x^{2}y+3x{y}^2)=(1000000+1331+330000+36300)-(1000000-1331-330000+36300)=1000000+1331+330000+36300-1000000+1331+330000-36300=1331+330000+1331+330000=662662$

Hence, ${111}^3-{89}^3=662662$.