Question

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

Answer 1

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**.