Multiply $ \dfrac{b}{10} $ by $ 2 $ to get $ \dfrac{ 2b }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{b}{10} \cdot 2 & \xlongequal{\text{Step 1}} \frac{b}{10} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ b \cdot 2 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2b }{ 10 } \end{aligned} $$

Multiply $ \dfrac{2b}{10} $ by $ \dfrac{a}{5} $ to get $ \dfrac{ 2ab }{ 50 } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2b}{10} \cdot \frac{a}{5} \xlongequal{\text{Step 1}} \frac{ 2b \cdot a }{ 10 \cdot 5 } \xlongequal{\text{Step 2}} \frac{ 2ab }{ 50 } \end{aligned} $$

Multiply $ \dfrac{2ab}{50} $ by $ b $ to get $ \dfrac{ 2ab^2 }{ 50 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2ab}{50} \cdot b & \xlongequal{\text{Step 1}} \frac{2ab}{50} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2ab \cdot b }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ab^2 }{ 50 } \end{aligned} $$

Add $ \dfrac{2}{a} $ and $ \dfrac{2ab^2}{50} $ to get $ \dfrac{ \color{purple}{ 2a^2b^2+100 } }{ 50a }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 50 }$ and the second by $\color{blue}{ a }$.

$$ \begin{aligned} \frac{2}{a} + \frac{2ab^2}{50} & = \frac{ 2 \cdot \color{blue}{ 50 }}{ a \cdot \color{blue}{ 50 }} + \frac{ 2ab^2 \cdot \color{blue}{ a }}{ 50 \cdot \color{blue}{ a }} = \\[1ex] &=\frac{ \color{purple}{ 100 } }{ 50a } + \frac{ \color{purple}{ 2a^2b^2 } }{ 50a }=\frac{ \color{purple}{ 2a^2b^2+100 } }{ 50a } \end{aligned} $$