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:

(4x25x+6)(x27)+(7x28x5) \left(-4x^2 - 5x + 6\right) - \left(x^2 - 7\right) + \left(-7x^2 - 8x - 5\right)

This becomes:

4x25x+6x2+77x28x5 -4x^2 - 5x + 6 - x^2 + 7 - 7x^2 - 8x - 5

Step 2: Combine Like Terms

Now, combine the like terms:

  • Combine the x2x^2 terms: 4x2x27x2=12x2-4x^2 - x^2 - 7x^2 = -12x^2
  • Combine the xx terms: 5x8x=13x-5x - 8x = -13x
  • Combine the constant terms: 6+75=86 + 7 - 5 = 8

Final Answer

The simplified expression is:

12x213x+8 \boxed{-12x^2 - 13x + 8}

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