If \[\left( \mathbf{a}+\mathbf{b} \right)=\mathbf{2}\] and \[\left( \mathbf{a}-\mathbf{b} \right)=\mathbf{10}.\] Find the value of \[\left( {{a}^{2}}+{{b}^{2}} \right)=10.\]

• A.  40    
• B.  52   
• C.  38    
• D.  42