Question
Perform the operation(s) and simplify completely.
(7x2−6x+2)−(4x−8)+(−6x2+3x)
(1 point)
Responses
x2−7x−6
x squared minus 7 x minus 6
x2−7x+10
x squared minus 7 x plus 10
13x2−13x+10
13 x squared minus 13 x plus 10
x2−13x+10
(7x2−6x+2)−(4x−8)+(−6x2+3x)
(1 point)
Responses
x2−7x−6
x squared minus 7 x minus 6
x2−7x+10
x squared minus 7 x plus 10
13x2−13x+10
13 x squared minus 13 x plus 10
x2−13x+10
Answers
GPT-4o mini
To simplify the expression \((7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)\), let's break it down step by step.
1. Distribute the negative sign in the second term:
\[
(7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x)
\]
2. Now combine all the terms:
\[
= 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x
\]
3. Group the like terms together:
- For \(x^2\) terms: \(7x^2 - 6x^2 = x^2\)
- For \(x\) terms: \(-6x - 4x + 3x = -7x\)
- Constant terms: \(2 + 8 = 10\)
4. Putting it all together:
\[
x^2 - 7x + 10
\]
The simplified expression is \(x^2 - 7x + 10\).
Thus, the correct response is:
**x²−7x+10**.
1. Distribute the negative sign in the second term:
\[
(7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x)
\]
2. Now combine all the terms:
\[
= 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x
\]
3. Group the like terms together:
- For \(x^2\) terms: \(7x^2 - 6x^2 = x^2\)
- For \(x\) terms: \(-6x - 4x + 3x = -7x\)
- Constant terms: \(2 + 8 = 10\)
4. Putting it all together:
\[
x^2 - 7x + 10
\]
The simplified expression is \(x^2 - 7x + 10\).
Thus, the correct response is:
**x²−7x+10**.