Certainly! Let’s simplify the given expression step-by-step and arrive at the final answer.
Given expression:
[tex]\[ x^2 + 8x - 33 - 42y - 4y^2 \][/tex]
### Step-by-Step Simplification
1. Identify and arrange like terms:
We can rearrange the terms to group the [tex]\(x\)[/tex]-terms, the [tex]\(y\)[/tex]-terms, and the constants together for better clarity:
[tex]\[ x^2 + 8x - 4y^2 - 42y - 33 \][/tex]
2. Combine and simplify:
The rearranged expression is already fully simplified, as there aren’t any like terms that can be combined further.
### Final Simplified Expression
Thus, the simplified form of the given expression is:
[tex]\[ x^2 + 8x - 4y^2 - 42y - 33 \][/tex]
This is the expression in its simplest form without any additional calculations needed.
