If a3 - b3 = 56 and a - b = 2, then the value of a2 + b2 will be?

Answer: Option B

$$\begin{array}{rl}& a^3-b^3=56\\ & \Rightarrow a-b=2\\ & \left(\text{By cubing}\right)\\ & \Rightarrow a^3-b^3-3ab\left(a-b\right)={\left(2\right)}^2\\ & \Rightarrow 56-3ab\times 2=8\\ & \Rightarrow -6ab=8-56\\ & \Rightarrow 6ab=48\\ & \Rightarrow ab=8\\ & \left(a-b\right)=2\\ & \left(\text{By squaring}\right)\\ & \Rightarrow {\left(a-b\right)}^2={\left(2\right)}^2\\ & \Rightarrow a^2+b^2-2ab=4\\ & \Rightarrow a^2+b^2=4+2ab\\ & \Rightarrow a^2+b^2=4+2\times 8\\ & \Rightarrow a^2+b^2=20\end{array}$$