Find the value of the expression `(9x^(2) + 24 x + 16)`, when x = 12

Answer

To find the value of the expression \(9x^2 + 24x + 16\) when \(x = 12\), we will follow these steps:

### Step 1: Substitute the value of \(x\)
We start by substituting \(x\) with \(12\) in the expression \(9x^2 + 24x + 16\).

\[ 9(12)^2 + 24(12) + 16 \]

### Step 2: Calculate \(12^2\)
Next, we calculate \(12^2\).

\[ 12^2 = 144 \]

### Step 3: Multiply \(9\) by \(144\)
Now we multiply \(9\) by \(144\).

\[ 9 \times 144 = 1296 \]

### Step 4: Calculate \(24 \times 12\)
Next, we calculate \(24 \times 12\).

\[ 24 \times 12 = 288 \]

### Step 5: Add all the terms together
Now we add all the calculated values together:

\[ 1296 + 288 + 16 \]

### Step 6: Perform the addition
First, add \(1296\) and \(288\):

\[ 1296 + 288 = 1584 \]

Now, add \(16\):

\[ 1584 + 16 = 1600 \]

### Final Answer
The value of the expression \(9x^2 + 24x + 16\) when \(x = 12\) is:

\[ \boxed{1600} \]

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