simplify (9x^2-6x+2)-(x^2+4x-39) what is the diffrence of the plynimials

1 answer

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we need to distribute the negative sign through the second polynomial 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, 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: \[ 2 + 39 = 41 \]

Putting it all together, we get:

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

So, the simplified difference of the polynomials is:

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