Coefficient of `x ^(2)` in ` (x + 9) (4-4x)` is

Options

A. 54
B. 4
C. `-30`
D. -4

Answer

To find the coefficient of \( x^2 \) in the expression \( (x + 9)(4 - 4x) \), we can follow these steps:

### Step 1: Expand the expression
We start by expanding the expression \( (x + 9)(4 - 4x) \).

\[ (x + 9)(4 - 4x) = x \cdot 4 + x \cdot (-4x) + 9 \cdot 4 + 9 \cdot (-4x) \]

### Step 2: Calculate each term
Now we calculate each of these products:

1. \( x \cdot 4 = 4x \)
2. \( x \cdot (-4x) = -4x^2 \)
3. \( 9 \cdot 4 = 36 \)
4. \( 9 \cdot (-4x) = -36x \)

### Step 3: Combine like terms
Now we combine all these terms:

\[ 4x - 4x^2 + 36 - 36x \]

Combine the \( x \) terms:

\[ -4x^2 + (4x - 36x) + 36 = -4x^2 - 32x + 36 \]

### Step 4: Identify the coefficient of \( x^2 \)
In the expression \( -4x^2 - 32x + 36 \), the coefficient of \( x^2 \) is the coefficient of the term \( -4x^2 \).

Thus, the coefficient of \( x^2 \) is:

\[ \text{Coefficient of } x^2 = -4 \]

### Final Answer
The coefficient of \( x^2 \) in the expression \( (x + 9)(4 - 4x) \) is \( -4 \).

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