Certainly! Let's solve the expression step-by-step:
We are given the expression:
[tex]\[ \left(9x^2 - 4x + 11\right) - \left(x^2 - 2x - 6\right) \][/tex]
### Step 1: Distribute the Negative Sign
Start by distributing the negative sign through the second polynomial:
[tex]\[ 9x^2 - 4x + 11 - x^2 + 2x + 6 \][/tex]
### Step 2: Combine Like Terms
Now, combine the like terms:
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 9x^2 - x^2 = 8x^2 \][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -4x + 2x = -2x \][/tex]
3. Combine the constant terms:
[tex]\[ 11 + 6 = 17 \][/tex]
### Step 3: Write the Resulting Polynomial
Putting all the combined terms together, we get:
[tex]\[ 8x^2 - 2x + 17 \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \boxed{8x^2 - 2x + 17} \][/tex]
