Factories:
`9y^(2) - 12y +4`

Answer

To factor the expression \( 9y^2 - 12y + 4 \), we can follow these steps:

### Step 1: Identify the coefficients
The expression is in the form of a quadratic equation \( ax^2 + bx + c \), where:
- \( a = 9 \)
- \( b = -12 \)
- \( c = 4 \)

### Step 2: Rewrite the expression
We can rewrite \( 9y^2 - 12y + 4 \) as:
\[ (3y)^2 - 12y + 4 \]

### Step 3: Recognize the pattern
Notice that \( 9y^2 - 12y + 4 \) can be recognized as a perfect square trinomial. It follows the pattern \( a^2 - 2ab + b^2 \), which factors to \( (a - b)^2 \).

### Step 4: Identify \( a \) and \( b \)
From the expression:
- \( a = 3y \)
- \( b = 2 \)

### Step 5: Apply the formula
Using the formula for the perfect square trinomial:
\[ (3y - 2)^2 \]

### Step 6: Write the final factored form
Thus, the factored form of \( 9y^2 - 12y + 4 \) is:
\[ (3y - 2)(3y - 2) \text{ or } (3y - 2)^2 \]

### Final Answer:
\[ 9y^2 - 12y + 4 = (3y - 2)^2 \]

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