Given a - b = 2, a3 - b3 = 26, then (a + b)2 is?

Answer: Option C

$$\begin{array}{rl}& a-b=2\\ & a^3-b^3=26\\ & \Rightarrow a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\\ & \Rightarrow 26=\left(2\right)\left(a^2+ab+b^2\right)\\ & \Rightarrow 13=\left(a^2+ab+b^2\right)....(i)\\ & \Rightarrow 4=13+ab\\ & \Rightarrow {\left(a-b\right)}^2=a^2+b^2-2ab\\ & \Rightarrow {\left(2\right)}^2=a^2+b^2+ab-3ab\\ & \Rightarrow 3ab=9\\ & \Rightarrow ab=3\\ & \therefore {\left(a+b\right)}^2\\ & ={\left(a-b\right)}^2+4ab\\ & =4+4\times 3\\ & =16\end{array}$$