Answer
See the explanation below.
Work Step by Step
Vectors are $u={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}$. Now, put vector $u$ in the expression $\left( c+d \right)u=cu+du$. Then, we get
$\begin{align}
& \left( c+d \right)\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right)=c\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right)+d\left( {{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j} \right) \\
& c{{a}_{1}}\mathbf{i}+c{{b}_{1}}\mathbf{i}+d{{a}_{1}}\mathbf{i}+d{{b}_{1}}\mathbf{j}=c{{a}_{1}}\mathbf{i}+c{{b}_{1}}\mathbf{j}+d{{a}_{1}}\mathbf{i}+d{{b}_{1}}\mathbf{j}
\end{align}$
Left side and right side are equal. Hence, $\left( c+d \right)u=cu+du$.
