To solve the expression [tex]\(\left(-2x^2 - 7\right) + \left(8x^2 - 3\right)\)[/tex], we will remove the parentheses and combine the like terms.
1. Start with the given expression:
[tex]\[
\left(-2x^2 - 7\right) + \left(8x^2 - 3\right)
\][/tex]
2. Remove the parentheses:
[tex]\[
-2x^2 - 7 + 8x^2 - 3
\][/tex]
3. Combine the like terms:
- For the [tex]\(x^2\)[/tex] terms: [tex]\( -2x^2 + 8x^2 \)[/tex]
- For the constant terms: [tex]\( -7 - 3 \)[/tex]
4. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-2x^2 + 8x^2 = 6x^2
\][/tex]
5. Combine the constant terms:
[tex]\[
-7 - 3 = -10
\][/tex]
So, the simplified expression after combining like terms is:
[tex]\[
6x^2 - 10
\][/tex]
Therefore, the result of the operation is [tex]\(6x^2 - 10\)[/tex].
