Question

without actually calculating the cubes find the value of 100³-60³-40³.

Answer 1

Use the identity : (a+b)³ = a³ + b³ + 3ab(a+b)
100 = 60+40

100³ = (60+40)³
⇒100³ = 60³ + 40³ + 3×60×40(60+40)
⇒100³ - 60³ - 40³ = 3×60×40×(60+40)
⇒100³ - 60³ - 40³ = 7200×(100)
⇒ 100³ - 60³ - 40³ = 720000

Answer 2

100³- 60³-40³
100³ = 40³+60³
100³ = (40+60)³
100³ = 60³ + 40³ + 3*40*60(40+60)
100³ - 60³ - 40³ = 3*40*60*(40+60)
100³ - 60³ - 40³ = 7200*100
100³ - 60³ - 40³ = 720000