Multiply $ \dfrac{a^2+13a+36}{a^2+2a-3} $ by $ \dfrac{a^2+7a-8}{a^2+18a+81} $ to get $ \dfrac{a^2+12a+32}{a^2+12a+27} $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{a^2+13a+36}{a^2+2a-3} \cdot \frac{a^2+7a-8}{a^2+18a+81} & \xlongequal{\text{Step 1}} \frac{ \left( a+4 \right) \cdot \color{blue}{ \left( a+9 \right) } }{ \left( a+3 \right) \cdot \color{red}{ \left( a-1 \right) } } \cdot \frac{ \left( a+8 \right) \cdot \color{red}{ \left( a-1 \right) } }{ \left( a+9 \right) \cdot \color{blue}{ \left( a+9 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ a+4 }{ a+3 } \cdot \frac{ a+8 }{ a+9 } \xlongequal{\text{Step 3}} \frac{ \left( a+4 \right) \cdot \left( a+8 \right) }{ \left( a+3 \right) \cdot \left( a+9 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ a^2+8a+4a+32 }{ a^2+9a+3a+27 } = \frac{a^2+12a+32}{a^2+12a+27} \end{aligned} $$