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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

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

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

x2−7x+10

1 answer

Let's perform the operations step by step:

  1. Start with the expression:
    \((7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)\)

  2. Distribute the negative sign in the second term:
    \((7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x)\)

  3. Combine like terms:

    • For \(x^2\) terms: \(7x^2 - 6x^2 = (7 - 6)x^2 = 1x^2\)
    • For \(x\) terms: \(-6x - 4x + 3x = (-6 - 4 + 3)x = -7x\)
    • For constant terms: \(2 + 8 = 10\)

  4. Putting it all together:
    The expression simplifies to:
    \(x^2 - 7x + 10\)

So the completely simplified form of the expression is:

Response: \(x^2 - 7x + 10\)