Multiply $ \dfrac{2}{5} $ by $ j^2 $ to get $ \dfrac{ 2j^2 }{ 5 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{2j^2}{5} $ from $ 5j $ to get $ \dfrac{ \color{purple}{ -2j^2+25j } }{ 5 }$.

Step 1: Write $ 5j $ 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 $\color{blue}{ 5 }$.

$$ \begin{aligned} 5j- \frac{2j^2}{5} & \xlongequal{\text{Step 1}} \frac{5j}{\color{red}{1}} - \frac{2j^2}{5} = \frac{ 5j \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} - \frac{ 2j^2 }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 25j } }{ 5 } - \frac{ \color{purple}{ 2j^2 } }{ 5 }=\frac{ \color{purple}{ -2j^2+25j } }{ 5 } \end{aligned} $$

Subtract $2j$ from $ \dfrac{-2j^2+25j}{5} $ to get $ \dfrac{ \color{purple}{ -2j^2+15j } }{ 5 }$.

Step 1: Write $ 2j $ 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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{-2j^2+25j}{5} -2j & \xlongequal{\text{Step 1}} \frac{-2j^2+25j}{5} - \frac{2j}{\color{red}{1}} = \frac{ -2j^2+25j }{ 5 } - \frac{ 2j \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2j^2+25j } }{ 5 } - \frac{ \color{purple}{ 10j } }{ 5 }=\frac{ \color{purple}{ -2j^2+15j } }{ 5 } \end{aligned} $$