Simplify:

(3x ^ 2 + 3/4 * x - 1) - (x ^ 2 - 1/4 * x)

A. 2x ^ 2 - 1/2 * x - 1

B. 2x ^ 2 + 1/2 * x - 1

C. 2x ^ 2 + x - 1

D. 4x ^ 2 + x - 1

1 answer

To simplify the expression \( (3x^2 + \frac{3}{4}x - 1) - (x^2 - \frac{1}{4}x) \), we first distribute the negative sign across the second set of parentheses:

\[ 3x^2 + \frac{3}{4}x - 1 - x^2 + \frac{1}{4}x \]

Next, we combine like terms.

  1. For the \( x^2 \) terms: \[ 3x^2 - x^2 = 2x^2 \]

  2. For the \( x \) terms: \[ \frac{3}{4}x + \frac{1}{4}x = \frac{3}{4}x + \frac{1}{4}x = \frac{4}{4}x = x \]

  3. The constant term remains the same: \[ -1 \]

Putting it all together, we have: \[ 2x^2 + x - 1 \]

Thus, the simplified expression is \( 2x^2 + x - 1 \).

The correct answer is C. \( 2x^2 + x - 1 \).