If a + b = 1, find the value of a³ + b³ - ab - (a² - b²)² = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}} \cr & a = 0 \cr & b = 1 \cr & \Rightarrow {a^3} + {b^3} - ab - {\left( {{a^2} - {b^2}} \right)^2} \cr & \Rightarrow 0 + 1 - 0 - {\left( {0 - 1} \right)^2} \cr & \Rightarrow 1 - 1 \cr & \Rightarrow 0 \cr} $$