## Simplifying the Expression: (8x^2 + 2x - 6) - (5x^2 - 3x + 2)

This problem involves simplifying an expression by subtracting two polynomials. Let's break down the steps:

### 1. Distribute the Negative Sign

The negative sign in front of the second parenthesis needs to be distributed to each term inside the parenthesis.

**(8x^2 + 2x - 6) - (5x^2 - 3x + 2)** becomes **(8x^2 + 2x - 6) - 5x^2 + 3x - 2**

### 2. Combine Like Terms

Now, we can combine the terms that have the same variable and exponent:

**x^2 terms:**8x^2 - 5x^2 =**3x^2****x terms:**2x + 3x =**5x****Constant terms:**-6 - 2 =**-8**

### 3. The Simplified Expression

Putting the combined terms together, the simplified expression is:

**3x^2 + 5x - 8**

### Conclusion

By distributing the negative sign and combining like terms, we successfully simplified the expression (8x^2 + 2x - 6) - (5x^2 - 3x + 2) to **3x^2 + 5x - 8**.