Middle School

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

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

Answer :

(3x^5 + 8x^3) - (7x^2 - 6x^3) = 3x^5 + 8x^3 - 7x^2 + 6x^3 = 3x^5 + 14x^3 - 7x^2

The expression [tex](3x^5 + 8x^3) - (7x^2 - 6x^3)[/tex] is equivalent to [tex]3x^5 + 14x^3 - 7x^2[/tex].

Given Expression:

[tex](3x^5 + 8x^3) - (7x^2 - 6x^3)[/tex]

To simplify the expression [tex](3x^5 + 8x^3) - (7x^2 - 6x^3)[/tex],distribute the negative sign to each term within the parentheses.

So, we can write the expression as

[tex]3x^5 + 8x^3 - 7x^2 + 6x^3.[/tex]

Next, combine like terms by adding or subtracting coefficients of the same degree.

In this case, the terms with the same degree are:

[tex]3x^5[/tex], [tex]8x^3[/tex], [tex]-7x^2[/tex], and [tex]6x^3[/tex].

Combining the like terms :

[tex]3x^5 + 8x^3 + 6x^3 - 7x^2.[/tex]

Finally, simplify by combining the coefficients:

[tex]3x^5 + (8x^3 + 6x^3) - 7x^2.[/tex]

Simplifying the coefficients, we have:

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

Therefore, the expression is [tex]3x^5 + 14x^3 - 7x^2[/tex].

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