To simplify the expression [tex]\(\left(3 x^2 - 2\right) + \left(2 x^2 - 6 x + 3\right)\)[/tex], follow these steps:
1. Distribute the addition across the parentheses, which effectively means removing the parentheses:
[tex]\[
3 x^2 - 2 + 2 x^2 - 6 x + 3
\][/tex]
2. Combine like terms. Like terms are the terms that contain the same variable raised to the same power. Here, we group the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3 x^2 + 2 x^2 = 5 x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms. There is only one [tex]\(x\)[/tex] term present:
[tex]\[
-6 x
\][/tex]
- Combine the constant terms:
[tex]\[
-2 + 3 = 1
\][/tex]
3. After combining all like terms, you get the simplified expression:
[tex]\[
5 x^2 - 6 x + 1
\][/tex]
The simplified form of the given expression is:
[tex]\[
5 x^2 - 6 x + 1
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{5 x^2 - 6 x + 1}
\][/tex]
