Factories:
`16x ^(2)- 24 x + 9`

Answer

To factor the expression \(16x^2 - 24x + 9\), we can follow these steps:

### Step 1: Identify the coefficients
The expression is in the standard quadratic form \(ax^2 + bx + c\), where:
- \(a = 16\)
- \(b = -24\)
- \(c = 9\)

### Step 2: Rewrite the expression
We want to express the quadratic in the form of a perfect square trinomial, which is \(a^2 - 2ab + b^2 = (a - b)^2\).

### Step 3: Break down the first term
The first term \(16x^2\) can be rewritten as \((4x)^2\).

### Step 4: Break down the last term
The last term \(9\) can be rewritten as \(3^2\).

### Step 5: Rewrite the middle term
Now, we need to express the middle term \(-24x\) in terms of \(4x\) and \(3\). We can see that:
\[ -24x = -2 \cdot (4x) \cdot 3 \]

### Step 6: Combine into a perfect square
Now we can rewrite the entire expression:
\[ 16x^2 - 24x + 9 = (4x)^2 - 2 \cdot (4x) \cdot 3 + 3^2 \]

### Step 7: Factor the perfect square
This matches the form of a perfect square trinomial, so we can factor it as:
\[ (4x - 3)^2 \]

### Final Answer
Thus, the factorization of \(16x^2 - 24x + 9\) is:
\[ (4x - 3)^2 \]

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