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High School Mathematics
6.19 Symmetric and Cyclic Expressions

Symmetric:
An expression f(x,y) is said to be symmetric if f(x,y) = f(y,x).

Example:
f(x,y) = ax + b + ay
If we interchange x and y, we can get the expression ay + b + ax which is same as ax + b + ay.

The sum, difference, product and quotient of two symmetric expressions are again symmetric

Cyclic Expressions:
An expression f(x,y,z) is said to be a cyclic expression if f(x,y,z) = f(y,z,x).
For the sake of brevity we use the symbols and to write the cyclic expressions.
is used for sum of terms and is used for product of terms.


Directions: Choose the correct answer. Also write at least 5 examples of your own.
Q 1: x3 + y3 + x2 + y2 + x + y, is this equation symmetry or not?
No
Yes

Q 2: Expand, a2b. (Variables 'a' and 'b')
b2a
(a2b)+(b2a)
a2b
(a2b)(b2a)

Question 3: This question is available to subscribers only!

Question 4: This question is available to subscribers only!


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