Questions: Simplify: (-4 x^2-5 x+6)-(x^2-7)+(-7 x^2-8 x-5)

Simplify: (-4 x^2-5 x+6)-(x^2-7)+(-7 x^2-8 x-5)
Transcript text: Simplify: \[ \left(-4 x^{2}-5 x+6\right)-\left(x^{2}-7\right)+\left(-7 x^{2}-8 x-5\right) \]
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Solution

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Solution Steps

Step 1: Distribute the Negative Sign

First, distribute the negative sign in the expression:

\[ \left(-4x^2 - 5x + 6\right) - \left(x^2 - 7\right) + \left(-7x^2 - 8x - 5\right) \]

This becomes:

\[ -4x^2 - 5x + 6 - x^2 + 7 - 7x^2 - 8x - 5 \]

Step 2: Combine Like Terms

Now, combine the like terms:

  • Combine the \(x^2\) terms: \(-4x^2 - x^2 - 7x^2 = -12x^2\)
  • Combine the \(x\) terms: \(-5x - 8x = -13x\)
  • Combine the constant terms: \(6 + 7 - 5 = 8\)

Final Answer

The simplified expression is:

\[ \boxed{-12x^2 - 13x + 8} \]

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