Perform the operation(s) and simplify completely. (7x2−6x+2)−(4x−8)+(−6x2+3x) (1 point) Responses 13x2−13x+10 13 x squared minus 13 x plus 10 x2−7x+10 x squared minus 7 x plus 10 x2−7x−6 x squared minus 7 x minus 6 x2−13x+10

1 answer

Let's simplify the expression step by step. The expression we need to simplify is:

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

  1. Distribute the negative sign in front of the second group:

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

Which simplifies to:

\[ 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x \]

  1. Combine like terms:
  • For \(x^2\) terms: \[ 7x^2 - 6x^2 = (7 - 6)x^2 = 1x^2 \text{ or simply } x^2 \]

  • For \(x\) terms: \[ -6x - 4x + 3x = (-6 - 4 + 3)x = -7x \]

  • For constant terms: \[ 2 + 8 = 10 \]

  1. Combine all simplified terms:

Putting it all together, we have:

\[ x^2 - 7x + 10 \]

Thus, the completely simplified expression is:

\[ \boxed{x^2 - 7x + 10} \]