If a + b = 10 and ab = 21, then the value of (a - b)2 is?

Answer: Option B

$$\begin{array}{rl}& a+b=10\text{ and }ab=21\\ & \left(a+b\right)=10\\ & \Rightarrow a^2+b^2+2ab=100\\ & \Rightarrow a^2+b^2=100-2ab\\ & \Rightarrow a^2+b^2=100-2\times 21\\ & \Rightarrow a^2+b^2=100-42\\ & a^2+b^2=58.........(i)\\ & {\left(a-b\right)}^2=a^2+b^2-2ab\\ & {\left(a-b\right)}^2=58-2\times 21\\ & \left[\text{from equation (i)}\right]\\ & =\text{58}-\text{42}\\ & {\left(a-b\right)}^2=16\end{array}$$