Simplify : `7x + 3x(x-4) = ?`
A. `10x + 12`
B. `10x - 12`
C. `3x^(2) + 5x`
D. `3x^(2) - 5x`

Options

A. D
B. C
C. A
D. B

Answer

To simplify the expression \( 7x + 3x(x - 4) \), we will follow these steps:

### Step 1: Distribute \( 3x \) in the term \( 3x(x - 4) \)
We start by distributing \( 3x \) to both terms inside the parentheses:

\[ 3x(x - 4) = 3x \cdot x - 3x \cdot 4 = 3x^2 - 12x \]

### Step 2: Substitute back into the original expression
Now, we can substitute this back into the original expression:

\[ 7x + 3x(x - 4) = 7x + (3x^2 - 12x) \]

### Step 3: Combine like terms
Next, we combine the like terms. The like terms here are \( 7x \) and \( -12x \):

\[ 7x - 12x = -5x \]

So, we now have:

\[ 3x^2 - 5x \]

### Final Result
Thus, the simplified expression is:

\[ 3x^2 - 5x \]

### Conclusion
The correct answer is option D: \( 3x^2 - 5x \).

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