Multiply $ \dfrac{1}{30} $ by $ 2k^3+9k^2+13k+9 $ to get $ \dfrac{ 2k^3+9k^2+13k+9 }{ 30 } $.

Step 1: Write $ 2k^3+9k^2+13k+9 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{30} \cdot 2k^3+9k^2+13k+9 & \xlongequal{\text{Step 1}} \frac{1}{30} \cdot \frac{2k^3+9k^2+13k+9}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( 2k^3+9k^2+13k+9 \right) }{ 30 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2k^3+9k^2+13k+9 }{ 30 } \end{aligned} $$

Multiply $ \dfrac{2k^3+9k^2+13k+9}{30} $ by $ 3k^2+9k+5 $ to get $ \dfrac{6k^5+45k^4+130k^3+189k^2+146k+45}{30} $.

Step 1: Write $ 3k^2+9k+5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2k^3+9k^2+13k+9}{30} \cdot 3k^2+9k+5 & \xlongequal{\text{Step 1}} \frac{2k^3+9k^2+13k+9}{30} \cdot \frac{3k^2+9k+5}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 2k^3+9k^2+13k+9 \right) \cdot \left( 3k^2+9k+5 \right) }{ 30 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 6k^5+18k^4+10k^3+27k^4+81k^3+45k^2+39k^3+117k^2+65k+27k^2+81k+45 }{ 30 } = \\[1ex] &= \frac{6k^5+45k^4+130k^3+189k^2+146k+45}{30} \end{aligned} $$