Let's simplify the expression:

$(4x^2 - 6x + 1) - (5x^2 + 8x + 6)$

Distribute the negative sign to each term inside the second parenthesis:

$4x^2 - 6x + 1 - 5x^2 - 8x - 6$

Now, combine like terms:

• For the $x^2$ terms: $4x^2 - 5x^2 = -x^2$
• For the $x$ terms: $-6x - 8x = -14x$
• For the constant terms: $1 - 6 = -5$

So, the simplified expression is:

$-x^2 - 14x - 5$

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How would you solve the equation $-x^2 - 14x - 5 = 0$?
2. What are the roots of the quadratic equation $x^2 + 14x + 5 = 0$?
3. How do you complete the square for $-x^2 - 14x - 5$?
4. What is the vertex form of the quadratic equation $-x^2 - 14x - 5$?
5. How can you graph the quadratic function $-x^2 - 14x - 5$?

Tip: When combining like terms, be careful with signs, especially when distributing a negative sign across a polynomial.