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

A. [tex]2x^6 + 7x^3[/tex]

B. [tex]3x^6 + x^5 - 3x^3[/tex]

C. [tex]3x^6 - x^5 - 3x^3[/tex]

D. [tex]3x^6 - x^5 + 7x^3[/tex]

Answer :

We start with the expression
[tex]$$
(3x^6 + 2x^3) - (x^5 - 5x^3).
$$[/tex]

Step 1: Distribute the negative sign across the second parentheses. This gives:
[tex]$$
3x^6 + 2x^3 - x^5 + 5x^3.
$$[/tex]

Step 2: Combine like terms. Notice that the terms involving [tex]$x^3$[/tex] can be added together:
[tex]$$
2x^3 + 5x^3 = 7x^3.
$$[/tex]

So the expression becomes:
[tex]$$
3x^6 - x^5 + 7x^3.
$$[/tex]

Step 3: Compare the result with the given options. The expression
[tex]$$
3x^6 - x^5 + 7x^3
$$[/tex]
matches the option:
[tex]$$
\text{Option D: } 3x^6 - x^5 + 7x^3.
$$[/tex]

Therefore, the equivalent expression is Option D.

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