Multiply $ \dfrac{3a^2b+12ab^3c-5ab}{8} $ by $ a $ to get $ \dfrac{12a^2b^3c+3a^3b-5a^2b}{8} $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3a^2b+12ab^3c-5ab}{8} \cdot a & \xlongequal{\text{Step 1}} \frac{3a^2b+12ab^3c-5ab}{8} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3a^2b+12ab^3c-5ab \right) \cdot a }{ 8 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3a^3b+12a^2b^3c-5a^2b }{ 8 } = \frac{12a^2b^3c+3a^3b-5a^2b}{8} \end{aligned} $$

Multiply $ \dfrac{12a^2b^3c+3a^3b-5a^2b}{8} $ by $ b $ to get $ \dfrac{ 12a^2b^4c+3a^3b^2-5a^2b^2 }{ 8 } $.

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.

$$ \begin{aligned} \frac{12a^2b^3c+3a^3b-5a^2b}{8} \cdot b & \xlongequal{\text{Step 1}} \frac{12a^2b^3c+3a^3b-5a^2b}{8} \cdot \frac{b}{\color{red}{1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 12a^2b^3c+3a^3b-5a^2b \right) \cdot b }{ 8 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 12a^2b^4c+3a^3b^2-5a^2b^2 }{ 8 } \end{aligned} $$