Use the Distributive Property to rewrite the expression and then simplify. 2(x2−x)+6x−3−7x

A. −x−3
B. 2x2−x−3
C. 2x2−3x−3
D. −4x

1 answer

To use the Distributive Property and simplify the expression \(2(x^2 - x) + 6x - 3 - 7x\), follow these steps:

  1. Apply the Distributive Property to the first term:

    \[ 2(x^2 - x) = 2x^2 - 2x \]

  2. Rewrite the expression with the simplified first term:

    \[ 2x^2 - 2x + 6x - 3 - 7x \]

  3. Combine like terms:

    • Combine the \(x\) terms: \(-2x + 6x - 7x\) \[ -2x + 6x = 4x \] \[ 4x - 7x = -3x \]
  4. Now, rewrite the entire expression with combined like terms:

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

So, the simplified expression is \(2x^2 - 3x - 3\).

The correct answer is C. 2x^2 - 3x - 3.