Algebraic Symmetry Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

f(x, y) = x^2 + y^2

symmetric in

x

and

y

1
Step 1: Check if $f(x, y) = f(y, x)$ .
2
Step 2: $f(y, x) = y^2 + x^2 = x^2 + y^2 = f(x, y)$ .
3
Step 3: Yes, it is symmetric — swapping $x$ and $y$ doesn't change the expression.

Answer

Yes,

f

is symmetric.

An expression is symmetric in

x

and

y

if swapping them produces the same expression. This symmetry often simplifies problem-solving — if

(a, b)

is a solution, so is

(b, a)

About Algebraic Symmetry

The property of an expression or equation that remains unchanged when certain transformations — such as swapping variables — are applied.

Is [formula] symmetric?

Is [formula] symmetric?

If [formula] and [formula], find [formula].