To determine which expression is equivalent to [tex]\(\left(3 x^5+8 x^3\right)-\left(7 x^2-6 x^3\right)\)[/tex], let's go through the subtraction step by step.
1. Write down the original expressions:
[tex]\[
\text{expr1} = 3x^5 + 8x^3
\][/tex]
[tex]\[
\text{expr2} = 7x^2 - 6x^3
\][/tex]
2. Subtract expr2 from expr1:
[tex]\[
(3x^5 + 8x^3) - (7x^2 - 6x^3)
\][/tex]
3. Distribute the negative sign through the second expression:
[tex]\[
3x^5 + 8x^3 - 7x^2 + 6x^3
\][/tex]
4. Combine like terms:
[tex]\[
3x^5 + (8x^3 + 6x^3) - 7x^2
\][/tex]
5. Perform the addition and subtraction within the parentheses:
[tex]\[
3x^5 + 14x^3 - 7x^2
\][/tex]
So, the equivalent expression is:
[tex]\[
3x^5 + 14x^3 - 7x^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C. \, 3x^5 + 14x^3 - 7x^2}
\][/tex]
