Verification of the Equation
To verify the equation x² y² = (x y) (x² - xy y²), we will simplify the right-hand side and check if it equals the left-hand side.
Step 1: Expand the Right-Hand Side
- Start with the expression: (x y) (x² - xy y²)
- Distribute (x y) across the terms in the parentheses:
- (x y) * x² = x³ y
- (x y) * (-xy y²) = -x² y³
- Combine these results:
- (x y) (x² - xy y²) = x³ y - x² y³
Step 2: Analyze the Left-Hand Side
- The left-hand side of the equation is x² y².
Step 3: Setting Both Sides Equal
- We have:
- Left-hand side: x² y²
- Right-hand side after expansion: x³ y - x² y³
- To check for equality, we can rearrange the right-hand side:
- x³ y - x² y³ = x² y (x - y²)
Step 4: Conclusion
- The expression x² y² does not equal x² y (x - y²) unless x = y².
- Therefore, the equation x² y² = (x y) (x² - xy y²) is not generally true.
Final Note
- Always ensure to simplify and check each side of an equation carefully to verify equality.