To simplify the expression [tex]\(\left(8 x^2-1+2 x^3\right)-\left(7 x^3-3 x^2+1\right)\)[/tex], follow these steps:
1. Expand the expression:
Distribute the negative sign through the second parenthesis:
[tex]\[
8 x^2 - 1 + 2 x^3 - (7 x^3 - 3 x^2 + 1)
\][/tex]
Which can be rewritten as:
[tex]\[
8 x^2 - 1 + 2 x^3 - 7 x^3 + 3 x^2 - 1
\][/tex]
2. Combine like terms:
Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
2 x^3 - 7 x^3 = -5 x^3
\][/tex]
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
8 x^2 + 3 x^2 = 11 x^2
\][/tex]
Combine the constant terms:
[tex]\[
-1 - 1 = -2
\][/tex]
3. Write the simplified expression:
Combining all the results together, we get:
[tex]\[
-5 x^3 + 11 x^2 - 2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-5 x^3 + 11 x^2 - 2
\][/tex]
So, the correct answer is:
[tex]\[
-5 x^3 + 11 x^2 - 2
\][/tex]
