Practice Algebraic Symmetry in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The property of an expression or equation that remains unchanged when certain transformations — such as swapping variables — are applied.
x^2 + y^2 is symmetric: swapping x and y gives the same expression.
Example 1
easyIs f(x, y) = x^2 + y^2 symmetric in x and y?
Example 2
mediumIs f(x, y) = x^2 - xy + y^2 symmetric?
Example 3
easyIs f(x, y) = x - y symmetric?
Example 4
mediumIf x + y = 10 and xy = 21, find x^2 + y^2.