To find the solution for the expression [tex]\(-q^3 r s^2 + 3 - q^7 r^2 + r^2 s^4\)[/tex], we first identify each term and its contribution to the final expression.
Step-by-Step Simplification:
1. Identify individual terms:
- The expression consists of four distinct terms:
1. [tex]\(-q^3 r s^2\)[/tex]
2. [tex]\(3\)[/tex]
3. [tex]\(-q^7 r^2\)[/tex]
4. [tex]\(r^2 s^4\)[/tex]
2. Combine the terms if possible:
- Note that these terms have different powers of [tex]\(q\)[/tex], [tex]\(r\)[/tex], and [tex]\(s\)[/tex], so they cannot be directly combined with each other. Each term is distinct and should be simplified separately if necessary.
Conclusion:
After careful consideration of the presented expression, we notice that no additional simplification or combining of terms is possible beyond the presentation as individual components. Therefore, the expression remains as:
[tex]\[
-q^3 r s^2 + 3 - q^7 r^2 + r^2 s^4
\][/tex]
So, the fully simplified form of the given expression is:
[tex]\[
-q^7 r^2 - q^3 r s^2 + r^2 s^4 + 3.
\][/tex]
This corresponds to reordering the terms in a standard way, typically from the highest degree of any variable to the lowest. The result given can be written as:
[tex]\[
-q^7 r^2 - q^3 r s^2 + r^2 s^4 + 3.
\][/tex]
