Answer
The scalar is $-40$.
Work Step by Step
The scalar $4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)$ can be obtained as,
$\begin{align}
& 4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)\mathbf{=}4\left( -\mathbf{i}+\mathbf{j} \right)\cdot \left[ 5\left( 3\mathbf{i}-2\mathbf{j} \right)-3\left( -5\mathbf{j} \right) \right] \\
& =\left( -4\mathbf{i}+4\mathbf{j} \right)\cdot \left( 15\mathbf{i}-10\mathbf{j}+15\mathbf{j} \right) \\
& =\left( -4\mathbf{i}+4\mathbf{j} \right)\cdot \left( 15\mathbf{i}+5\mathbf{j} \right) \\
& =\left( -4 \right)\cdot 15+4\cdot 5
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& 4\mathbf{u}\cdot \left( 5\mathbf{v-}3\mathbf{w} \right)=\left( -4 \right)\cdot 15+4\cdot 5 \\
& =-60+20 \\
& =-40
\end{align}$
Hence, the scalar of $4\mathbf{u}\cdot \left( 5\mathbf{v}-3\mathbf{w} \right)$ is $-40$.
