Which of the following epression is equaivalent to `a(4-a) - 5(a + 7)`?

Options

A. `-2a - 35`
B. `-2a + 7`
C. `-a^(2) - a - 35`
D. `-a^(2) - a + 7`

Answer

To find the expression equivalent to \( a(4-a) - 5(a + 7) \), we can follow these steps:

### Step 1: Distribute the terms
We start by distributing \( a \) in the first part of the expression and \( -5 \) in the second part:
\[ a(4 - a) = 4a - a^2 \]
\[ -5(a + 7) = -5a - 35 \]

### Step 2: Combine the results
Now, we combine the results from Step 1:
\[ 4a - a^2 - 5a - 35 \]

### Step 3: Group like terms
Next, we group the like terms together:
\[ (-a^2) + (4a - 5a) - 35 \]

### Step 4: Simplify the expression
Now we simplify the expression:
\[ -a^2 - a - 35 \]

### Final Expression
Thus, the expression equivalent to \( a(4-a) - 5(a + 7) \) is:
\[ -a^2 - a - 35 \]