Add $s$ and $ \dfrac{1}{10} $ to get $ \dfrac{ \color{purple}{ 10s+1 } }{ 10 }$.

Step 1: Write $ s $ 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 $\color{blue}{ 10 }$.

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

Multiply $10$ by $ \dfrac{10s+1}{10} $ to get $ 10s+1$.

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

Step 2: Cancel $ \color{blue}{ 10 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{10s+1}{10} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{10s+1}{10} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{10s+1}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( 10s+1 \right) }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 10s+1 }{ 1 } =10s+1 \end{aligned} $$

Multiply each term of $ \left( \color{blue}{10s+1}\right) $ by each term in $ \left( s+6\right) $.

$$ \left( \color{blue}{10s+1}\right) \cdot \left( s+6\right) = 10s^2+60s+s+6 $$

Combine like terms:

$$ 10s^2+ \color{blue}{60s} + \color{blue}{s} +6 = 10s^2+ \color{blue}{61s} +6 $$

$$ \left( \color{blue}{10s^2+61s+6}\right) \cdot k = 10ks^2+61ks+6k $$