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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

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 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.