Understanding the Product of xy, yz, zx
To find the product of the expressions xy, yz, and zx, we follow a straightforward multiplication process.
Step-by-Step Calculation
- Identify the expressions: We have three expressions:
- xy
- yz
- zx
- Multiply the expressions: The product of these three can be expressed as:
- (xy) * (yz) * (zx)
- Rearranging the terms: When multiplying, we can rearrange the terms as follows:
- x * y * y * z * z * x
- Combine like terms: This simplifies to:
- x^2 * y^2 * z
Thus, the final expression for the product of xy, yz, and zx is:
- x^2 * y^2 * z
Final Expression
The complete product of the three expressions can be succinctly represented as:
- x^2 * y^2 * z
Conclusion
By breaking down the multiplication of the expressions xy, yz, and zx, we can derive a simplified algebraic expression. This approach not only clarifies the relationship between variables but also emphasizes the importance of organization in algebraic manipulation. Understanding these fundamentals is crucial for tackling more complex algebraic problems in examinations such as UPSC.