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Perform the operation(s) and simplify completely.

(7x2−6x+2)−(4x−8)+(−6x2+3x)

(1 point)
Responses

x2−7x+10
x squared minus 7 x plus 10

x2−7x−6
x squared minus 7 x minus 6

x2−13x+10
x squared minus 13 x plus 10

13x2−13x+10

1 answer

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 front of \((4x - 8)\): \[ (7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x) \]

  2. Combine like terms:

    • \(7x^2 - 6x^2\) gives us \(1x^2\) or \(x^2\).
    • \(-6x - 4x + 3x\) gives us \(-7x\).
    • \(2 + 8\) gives us \(10\).

Putting it all together, we have: \[ x^2 - 7x + 10 \]

Thus, the simplified expression is: \[ \boxed{x^2 - 7x + 10} \]