To simplify the given expression [tex]\(\left(17x^2 + 7x - 14\right) - \left(-6x^2 - 5x - 18\right)\)[/tex], follow these steps:
1. Distribute the negative sign through the second polynomial:
This means changing the sign of each term inside the parentheses of the second polynomial:
[tex]\[
\left(17x^2 + 7x - 14\right) - \left(-6x^2 - 5x - 18\right) \implies \left(17x^2 + 7x - 14\right) + \left(6x^2 + 5x + 18\right)
\][/tex]
2. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
17x^2 + 6x^2 = 23x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
7x + 5x = 12x
\][/tex]
- Combine the constant terms:
[tex]\[
-14 + 18 = 4
\][/tex]
3. Write the simplified expression:
By combining the like terms, we get:
[tex]\[
23x^2 + 12x + 4
\][/tex]
Thus, the simplified form of the given expression is [tex]\(\boxed{23x^2 + 12x + 4}\)[/tex].
