To simplify the expression \((7x^2−6x+2)−(4x−8)+(−6x^2+3x)\), let's first distribute any negative signs and then combine like terms.
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Distribute the negative sign in the second part of the expression: \[ (7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x) = 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x \]
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Now, combine like terms:
- For \(x^2\) terms: \(7x^2 - 6x^2 = 1x^2\)
- For \(x\) terms: \(-6x - 4x + 3x = -7x\)
- For constant terms: \(2 + 8 = 10\)
Putting it all together, we have: \[ 1x^2 - 7x + 10 \]
- The final simplified expression is: \[ x^2 - 7x + 10 \]
This expression can be left as is or factored if necessary.
- Factoring \(x^2 - 7x + 10\) gives: \[ (x - 5)(x - 2) \]
Thus, the completely simplified form of the original expression is: \[ (x - 5)(x - 2) \quad \text{or} \quad x^2 - 7x + 10 \]