Question

simplifying the following
(6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1)

Answer 1

To simplify the expression \((6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1)\), we first distribute the negative sign in front of the second set of parentheses:

\[
(6x^3 + 2x^2 - 5x - 14) + (5x^3 - 7x^2 - 2x + 1)
\]

Next, we can combine like terms:

1. Combine the \(x^3\) terms:
\[
6x^3 + 5x^3 = 11x^3
\]

2. Combine the \(x^2\) terms:
\[
2x^2 - 7x^2 = -5x^2
\]

3. Combine the \(x\) terms:
\[
-5x - 2x = -7x
\]

4. Combine the constant terms:
\[
-14 + 1 = -13
\]

Now, putting it all together, we have:

\[
11x^3 - 5x^2 - 7x - 13
\]

Thus, the simplified expression is:

\[
\boxed{11x^3 - 5x^2 - 7x - 13}
\]