Multiply $8$ by $ \dfrac{j}{3} $ to get $ \dfrac{ 8j }{ 3 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{j}{3} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{j}{3} \xlongequal{\text{Step 2}} \frac{ 8 \cdot j }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 8j }{ 3 } \end{aligned} $$

Multiply $ \dfrac{8j}{3} $ by $ j $ to get $ \dfrac{ 8j^2 }{ 3 } $.

Step 1: Write $ j $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8j}{3} \cdot j & \xlongequal{\text{Step 1}} \frac{8j}{3} \cdot \frac{j}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8j \cdot j }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8j^2 }{ 3 } \end{aligned} $$

Subtract $ \dfrac{8j^2}{3} $ from $ 5j^2 $ to get $ \dfrac{ \color{purple}{ 7j^2 } }{ 3 }$.

Step 1: Write $ 5j^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 5j^2- \frac{8j^2}{3} & \xlongequal{\text{Step 1}} \frac{5j^2}{\color{red}{1}} - \frac{8j^2}{3} = \frac{ 5j^2 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ 8j^2 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 15j^2 } }{ 3 } - \frac{ \color{purple}{ 8j^2 } }{ 3 }=\frac{ \color{purple}{ 7j^2 } }{ 3 } \end{aligned} $$