Certainly! Let's solve the given problem step by step.
We start with the equation:
[tex]\[ a^2 + b^2 = 417 \][/tex]
Our goal is to find [tex]\((ab)^2\)[/tex].
1. Define the variables and given information:
- We are given [tex]\( a^2 + b^2 = 417 \)[/tex].
- We need to find [tex]\((ab)^2\)[/tex].
2. Substitute and simplify:
- We know that the product [tex]\(ab\)[/tex] is the value we’re interested in.
- By squaring [tex]\( ab \)[/tex], we get [tex]\((ab)^2\)[/tex].
3. Relationship between given and required values:
- However, there's no straightforward way to determine [tex]\(ab\)[/tex] directly from [tex]\( a^2 + b^2 = 417 \)[/tex] without additional information such as another equation relating [tex]\(a\)[/tex] and [tex]\(b\)[/tex]. Typically, in problems involving sums of squares, one might assume there’s another constraint or use the properties of the numbers involved.
4. What have we calculated:
- Given [tex]\( a^2 + b^2 = 417 \)[/tex], the desired outcome is to express [tex]\( (ab)^2 \)[/tex] in some form, typically involving [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
5. Conclusion:
- Conclusively, the result can be simplified algebraically. From the combined analysis of the expression, it directly relates to [tex]\(a\)[/tex] and [tex]\(b\)[/tex], which involves the squared product form:
Therefore, [tex]\((ab)^2 = a^2 b^2\)[/tex].
Thus, the step-by-step result derived:
[tex]\[ (ab)^2 = a^2 b^2 \][/tex]
