Coefficient of `x ^(2)` in `(x +7) (5-3) (3x -6)` is

Options

A. 96
B. `-30`
C. 42
D. `-18`

Answer

To find the coefficient of \( x^2 \) in the expression \( (x + 7)(5 - 3)(3x - 6) \), we will follow these steps:

### Step 1: Simplify the constants
First, we simplify the constant part of the expression:
\[ 5 - 3 = 2 \]
Now, we can rewrite the expression as:
\[ (x + 7)(2)(3x - 6) \]

### Step 2: Distribute the constant
Next, we can distribute the constant \( 2 \) into the expression:
\[ 2(x + 7)(3x - 6) \]

### Step 3: Expand the first bracket
Now, we will expand \( (x + 7)(3x - 6) \):
\[ (x + 7)(3x - 6) = x(3x - 6) + 7(3x - 6) \]
Calculating each part:
\[ = 3x^2 - 6x + 21x - 42 \]
Combining like terms:
\[ = 3x^2 + 15x - 42 \]

### Step 4: Multiply by the constant
Now, we multiply the entire expression by \( 2 \):
\[ 2(3x^2 + 15x - 42) = 6x^2 + 30x - 84 \]

### Step 5: Identify the coefficient of \( x^2 \)
The coefficient of \( x^2 \) in the final expression \( 6x^2 + 30x - 84 \) is:
\[ 6 \]

### Final Answer
Thus, the coefficient of \( x^2 \) in the expression \( (x + 7)(5 - 3)(3x - 6) \) is \( 6 \).

---