Simplify the Quadratic Expression: 9x²-12x+4

To rewrite the expression $9x^2 - 12x + 4$ as a perfect square, follow these steps:

• Step 1: Compare the expression $9x^2 - 12x + 4$ with $(a - b)^2$.
• Step 2: Note that $(a - b)^2 = a^2 - 2ab + b^2$.
• Step 3: Identify matching terms: $a^2 = 9x^2$, $-2ab = -12x$, $b^2 = 4$.

Now, separate this into steps:
Step 1: Set $a^2 = 9x^2$, so $a = 3x$.
Step 2: Set $b^2 = 4$, so $b = 2$.
Step 3: Verify $-2ab = -12x$:
$-2 \times 3x \times 2 = -12x.$
This confirms our values of $a$ and $b$ are correct.

Thus, the expression $9x^2 - 12x + 4$ is equivalent to the square $(3x - 2)^2$.

The correct choice is: $(3x-2)^2$.