Question

Which expression is equivalent to (3x^5+7x^2+10x^3)-(7x^2-4x^3+7x^5)

Answer 1

To simplify the expression \((3x^5 + 7x^2 + 10x^3) - (7x^2 - 4x^3 + 7x^5)\), we first distribute the negative sign across the terms in the second set of parentheses:

\[
(3x^5 + 7x^2 + 10x^3) - 7x^2 + 4x^3 - 7x^5
\]

Now, we can combine like terms:

1. For \(x^5\) terms:
\[
3x^5 - 7x^5 = -4x^5
\]

2. For \(x^3\) terms:
\[
10x^3 + 4x^3 = 14x^3
\]

3. For \(x^2\) terms:
\[
7x^2 - 7x^2 = 0
\]

Putting it all together, we have:

\[
-4x^5 + 14x^3 + 0 = -4x^5 + 14x^3
\]

Thus, the expression equivalent to \((3x^5 + 7x^2 + 10x^3) - (7x^2 - 4x^3 + 7x^5)\) is:

\[
-4x^5 + 14x^3
\]