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

Answer: Option A

$$\begin{array}{rl}& \text{Let}\\ & a=0\\ & b=1\\ & \Rightarrow a^3+b^3-ab-{\left(a^2-b^2\right)}^2\\ & \Rightarrow 0+1-0-{\left(0-1\right)}^2\\ & \Rightarrow 1-1\\ & \Rightarrow 0\end{array}$$