Simplify (9x^2−6x+2)−(x^2+4x−39)

Question

.(1 point)
The difference of the polynomials is
.

Answer 1

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we first distribute the negative sign across the second polynomial:

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

Next, we combine like terms:

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

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

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

Now we can put it all together:

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

Thus, the simplified expression is:

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