Simplify : `3x(x+4) - x(x-2)`

Options

A. `2x^(2) + 14x`
B. `4x^(2) - 14x`
C. `4x^(2) + 14x`
D. `2x^(2) - 14x`

Answer

To simplify the expression \( 3x(x + 4) - x(x - 2) \), we will follow these steps:

### Step 1: Distribute the terms
First, we will distribute \( 3x \) to both terms inside the first parentheses and \( -x \) to both terms inside the second parentheses.

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

### Step 2: Combine the results
Now, we will combine the results from Step 1:

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

This simplifies to:

\[ 3x^2 + 12x - x^2 + 2x \]

### Step 3: Combine like terms
Now we will combine like terms:

- For \( x^2 \) terms: \( 3x^2 - x^2 = 2x^2 \)
- For \( x \) terms: \( 12x + 2x = 14x \)

Putting it all together, we get:

\[ 2x^2 + 14x \]

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

\[ \boxed{2x^2 + 14x} \]

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