On taking the \( LHS\) side and expanding it further,
\( LHS={\left(a+b\right)}^{2}\)
\( =\left(a+b\right)\left(a+b\right)\)
\( =a\left(a+b\right)+b\left(a+b\right)\)
\( ={a}^{2}+ab+ba+{b}^{2}\)
\( ={a}^{2}+ab+ab+{b}^{2}\)
\( ={a}^{2}+2ab+{b}^{2}\)
\( =RHS\)
Hence, proved.