Question

Simplify (9x^2-6x+2)-(x^2+4x-39).(1 point)
The difference of the polynomials is

Answer 1

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we will first distribute the negative sign to the second polynomial and then combine like terms.

1. Rewrite the expression:
\[
9x^2 - 6x + 2 - (x^2 + 4x - 39)
\]

2. Distribute the negative sign:
\[
9x^2 - 6x + 2 - x^2 - 4x + 39
\]

3. Now, combine like terms:
- For \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
- For \(x\) terms: \(-6x - 4x = -10x\)
- For constant terms: \(2 + 39 = 41\)

So combining these gives:
\[
8x^2 - 10x + 41
\]

Thus, the simplified difference of the polynomials is:
\[
\boxed{8x^2 - 10x + 41}
\]