Multiply $a^2b^2$ by $ \dfrac{c+2}{a} $ to get $ \dfrac{ a^2b^2c+2a^2b^2 }{ a } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{a^2b^2c+2a^2b^2}{a} $ by $ b $ to get $ \dfrac{ a^2b^3c+2a^2b^3 }{ a } $.

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.

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

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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