1. **State the problem:** Factorize the expression $9x^2 - 12xy + 4y^2$. 2. **Recognize the form:** This is a quadratic expression in two variables. It resembles the form of a perfect square trinomial $a^2 - 2ab + b^2 = (a - b)^2$. 3. **Identify terms:** - $9x^2 = (3x)^2$ - $4y^2 = (2y)^2$ - The middle term is $-12xy$, which should be $-2 \times 3x \times 2y = -12xy$ to fit the perfect square pattern. 4. **Apply the formula:** Since the middle term matches, the expression can be factored as $$9x^2 - 12xy + 4y^2 = (3x - 2y)^2$$ 5. **Final answer:** $$\boxed{(3x - 2y)^2}$$