Simplify (9x squared- 6X + 2) - (x squared plus 4x - 39)

Question

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 across the second polynomial and then combine like terms.

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

2. Now, combine like terms:

   • Combine the \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
   • Combine the \(x\) terms: \(-6x - 4x = -10x\)
   • Combine the constant terms: \(2 + 39 = 41\)

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

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