What is the value of ( a^2 + b^2 ) ( a - b ) - ( a^3 - b^3 )a^2b - ab^2?

Answer: Option C

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