Multiplying rational expressions example shown on a whiteboard.

- Factor each polynomial in the numerators and denominators.
- The first numerator, $x^2 - 8x + 12$, factors to $(x - 6)(x - 2)$.
- The first denominator, $x^2 - 16$, is a difference of squares and factors to $(x - 4)(x + 4)$.
- The second numerator, $4x + 16$, has a common factor of 4, factoring to $4(x + 4)$.
- The second denominator, $x^2 - 4x + 4$, is a perfect square trinomial and factors to $(x - 2)^2$.
- Rewrite the expression with the factored forms: $\frac{(x - 6)(x - 2)}{(x - 4)(x + 4)} \cdot \frac{4(x + 4)}{(x - 2)^2}$.
- Cancel common factors between numerators and denominators: cancel one $(x - 2)$ and the $(x + 4)$.
- Multiply the remaining factors: $\frac{(x - 6) \cdot 4}{(x - 4) \cdot (x - 2)}$.
- Write the final simplified expression: $\frac{4(x - 6)}{(x - 4)(x - 2)}$.