Question

Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is

Answer 1

Distribute the subtraction (−1), then combine like terms.

Answer 2

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

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

2. Combine like terms:
- For the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]
- For the \(x\) terms:
\[
-6x - 4x = -10x
\]
- For the constant terms:
\[
2 + 39 = 41
\]

3. Putting it all together:
\[
8x^2 - 10x + 41
\]

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

Answer 3

To distribute the subtraction (−1) and combine like terms for the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we will follow these steps:

1. **Distribute the negative sign** to the second polynomial:
\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - 1 \cdot x^2 - 1 \cdot 4x + 1 \cdot 39
\]
This becomes:
\[
9x^2 - 6x + 2 - x^2 - 4x + 39
\]

2. **Combine like terms**:
- For the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]
- For the \(x\) terms:
\[
-6x - 4x = -10x
\]
- For the constant terms:
\[
2 + 39 = 41
\]

3. **Putting it all together**:
\[
8x^2 - 10x + 41
\]

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