Question
Add or subtract to simplify
(X^5+x^3)-(6x-x^3+6x^5)
(X^5+x^3)-(6x-x^3+6x^5)
Answers
GPT-4o mini
To simplify the expression \((x^5 + x^3) - (6x - x^3 + 6x^5)\), let's first distribute the negative sign across the terms inside the parentheses:
\[
(x^5 + x^3) - (6x - x^3 + 6x^5) = x^5 + x^3 - 6x + x^3 - 6x^5
\]
Now, combine like terms:
1. Combine the \(x^5\) terms: \(x^5 - 6x^5 = -5x^5\)
2. Combine the \(x^3\) terms: \(x^3 + x^3 = 2x^3\)
3. The \(6x\) term remains as \(-6x\).
Putting it all together, we have:
\[
-5x^5 + 2x^3 - 6x
\]
So, the simplified expression is:
\[
-5x^5 + 2x^3 - 6x
\]
\[
(x^5 + x^3) - (6x - x^3 + 6x^5) = x^5 + x^3 - 6x + x^3 - 6x^5
\]
Now, combine like terms:
1. Combine the \(x^5\) terms: \(x^5 - 6x^5 = -5x^5\)
2. Combine the \(x^3\) terms: \(x^3 + x^3 = 2x^3\)
3. The \(6x\) term remains as \(-6x\).
Putting it all together, we have:
\[
-5x^5 + 2x^3 - 6x
\]
So, the simplified expression is:
\[
-5x^5 + 2x^3 - 6x
\]