Multiply $35$ by $ \dfrac{x}{20} $ to get $ \dfrac{ 35x }{ 20 } $.

Step 1: Write $ 35 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 35 \cdot \frac{x}{20} & \xlongequal{\text{Step 1}} \frac{35}{\color{red}{1}} \cdot \frac{x}{20} \xlongequal{\text{Step 2}} \frac{ 35 \cdot x }{ 1 \cdot 20 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 35x }{ 20 } \end{aligned} $$

Multiply $ \dfrac{35x}{20} $ by $ x $ to get $ \dfrac{ 35x^2 }{ 20 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{35x}{20} \cdot x & \xlongequal{\text{Step 1}} \frac{35x}{20} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 35x \cdot x }{ 20 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 35x^2 }{ 20 } \end{aligned} $$

Add $10$ and $ \dfrac{35x^2}{20} $ to get $ \dfrac{ \color{purple}{ 35x^2+200 } }{ 20 }$.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 20 }$.

$$ \begin{aligned} 10+ \frac{35x^2}{20} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} + \frac{35x^2}{20} = \frac{ 10 \cdot \color{blue}{ 20 }}{ 1 \cdot \color{blue}{ 20 }} + \frac{ 35x^2 }{ 20 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 200 } }{ 20 } + \frac{ \color{purple}{ 35x^2 } }{ 20 }=\frac{ \color{purple}{ 35x^2+200 } }{ 20 } \end{aligned} $$