1. **State the problem:** Factor the perfect square trinomial $4x^2 - 12x + 9$. 2. **Recall the formula for a perfect square trinomial:** $$a^2 - 2ab + b^2 = (a - b)^2$$ This means the trinomial can be expressed as the square of a binomial. 3. **Identify $a$ and $b$:** - $4x^2$ is a perfect square: $4x^2 = (2x)^2$ - $9$ is a perfect square: $9 = 3^2$ 4. **Check the middle term:** The middle term should be $-2ab = -2 \times 2x \times 3 = -12x$, which matches the given middle term. 5. **Write the factorization:** $$4x^2 - 12x + 9 = (2x - 3)^2$$ **Final answer:** $(2x - 3)^2$