Which expression is equivalent to [tex]\left(3 x^5+8 x^3\right)-\left(7 x^2-6 x^3\right)[/tex]?

A. [tex]-4 x^3+14[/tex]

B. [tex]-4 x^5+14 x^3[/tex]

C. [tex]3 x^5+14 x^3-7 x^2[/tex]

D. [tex]3 x^5+2 x^3-7 x^2[/tex]



Answer :

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]