Question

Simplify (9x2−6x+2)−(x2+4x−39)

Answer 1

To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we need to distribute the negative sign through the second set of parentheses and then combine like terms.

Starting with the expression:

\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39)
\]

Distributing the negative sign:

\[
= 9x^2 - 6x + 2 - x^2 - 4x + 39
\]

Now, we can combine like terms. We'll group them by the powers of \(x\):

1. Combine \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]

2. Combine \(x\) terms:
\[
-6x - 4x = -10x
\]

3. Combine constant terms:
\[
2 + 39 = 41
\]

Putting it all together, we have:

\[
8x^2 - 10x + 41
\]

Thus, the simplified expression is:

\[
\boxed{8x^2 - 10x + 41}
\]