Square of ` 3 (6 - 2 x) ` is

Options

A. `12 x ^(2) - 72 x + 108`
B. ` 4 x ^(2) - 24 x + 36`
C. ` 108 - 72 x - 12 x^(2)`
D. ` 36 x^(2) - 216 x + 324 `

Answer

To find the square of \( 3(6 - 2x) \), we will follow these steps:

### Step 1: Write the expression
We start with the expression we need to square:
\[ (3(6 - 2x))^2 \]

### Step 2: Apply the square
Using the property of squares, we can rewrite this as:
\[ = 3^2 \cdot (6 - 2x)^2 \]

### Step 3: Calculate \( 3^2 \)
Calculating \( 3^2 \):
\[ 3^2 = 9 \]
So, we now have:
\[ = 9 \cdot (6 - 2x)^2 \]

### Step 4: Expand \( (6 - 2x)^2 \)
Now we need to expand \( (6 - 2x)^2 \) using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \):
\[ (6 - 2x)^2 = 6^2 - 2 \cdot 6 \cdot 2x + (2x)^2 \]
Calculating each term:
- \( 6^2 = 36 \)
- \( -2 \cdot 6 \cdot 2x = -24x \)
- \( (2x)^2 = 4x^2 \)

Putting it all together:
\[ (6 - 2x)^2 = 36 - 24x + 4x^2 \]

### Step 5: Substitute back into the expression
Now substitute this back into our expression:
\[ 9 \cdot (36 - 24x + 4x^2) \]

### Step 6: Distribute the 9
Now distribute the 9:
\[ = 9 \cdot 36 - 9 \cdot 24x + 9 \cdot 4x^2 \]
Calculating each term:
- \( 9 \cdot 36 = 324 \)
- \( -9 \cdot 24x = -216x \)
- \( 9 \cdot 4x^2 = 36x^2 \)

Putting it all together:
\[ = 36x^2 - 216x + 324 \]

### Final Answer
Thus, the square of \( 3(6 - 2x) \) is:
\[ 36x^2 - 216x + 324 \]

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