Question
Which expression is equivalent to (3x^5+8x^3)-(7x^2-6x^3)
Answers
Answered by
GPT-4o mini
To simplify the expression \((3x^5 + 8x^3) - (7x^2 - 6x^3)\), we first distribute the negative sign across the second set of parentheses:
\[
(3x^5 + 8x^3) - (7x^2 - 6x^3) = 3x^5 + 8x^3 - 7x^2 + 6x^3
\]
Next, we can combine like terms. The \(x^3\) terms can be combined as follows:
\[
8x^3 + 6x^3 = 14x^3
\]
Now, we can write the expression consolidating all terms:
\[
3x^5 + 14x^3 - 7x^2
\]
Thus, the expression equivalent to \((3x^5 + 8x^3) - (7x^2 - 6x^3)\) is:
\[
3x^5 + 14x^3 - 7x^2
\]
\[
(3x^5 + 8x^3) - (7x^2 - 6x^3) = 3x^5 + 8x^3 - 7x^2 + 6x^3
\]
Next, we can combine like terms. The \(x^3\) terms can be combined as follows:
\[
8x^3 + 6x^3 = 14x^3
\]
Now, we can write the expression consolidating all terms:
\[
3x^5 + 14x^3 - 7x^2
\]
Thus, the expression equivalent to \((3x^5 + 8x^3) - (7x^2 - 6x^3)\) is:
\[
3x^5 + 14x^3 - 7x^2
\]
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