Certainly! Let's simplify the expression [tex]\((8 x^2 - 1 + 2 x^3) - (7 x^3 - 3 x^2 + 1)\)[/tex] step by step.
1. Write down the original expression:
[tex]\[
(8x^2 - 1 + 2x^3) - (7x^3 - 3x^2 + 1)
\][/tex]
2. Distribute the negative sign across the second polynomial:
[tex]\[
8x^2 - 1 + 2x^3 - 7x^3 + 3x^2 - 1
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
2x^3 - 7x^3 = -5x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
8x^2 + 3x^2 = 11x^2
\][/tex]
- Combine the constant terms:
[tex]\[
-1 - 1 = -2
\][/tex]
4. Write the simplified expression:
[tex]\[
-5x^3 + 11x^2 - 2
\][/tex]
Thus, the simplified expression is:
[tex]\[
-5x^3 + 11x^2 - 2
\][/tex]
So, the correct option is:
[tex]\[
-5x^3 + 11x^2 - 2
\][/tex]
