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### High School Mathematics6.19 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 å and Õ to write the cyclic expressions.
å is used for sum of terms and Õ is used for product of terms.

Directions: Choose the correct answer. Also write at least 5 examples of your own.
 Q 1: x2 + y2 + z2, is this equation symmetry or not?YesNo Q 2: x3 + 3x2y + xy2 + y3, is this equation symmetry or not?YesNo Q 3: x3 + y3 + x2 + y2 + x + y, is this equation symmetry or not?YesNo Q 4: Expand, å a2b. (Variables 'a' and 'b')a2b + b2aa2bb2aa2b + ba Q 5: Expand, Õ a2b. (Variables 'a' and 'b')a2b(a2b)(b2a)b2a(a2b)+(b2a) Q 6: Expand, å a2b. (Variables a, b, c and d)a2b +b2c + c2d + d2aa2b +b2c + c2da2b + d2ab2c + c2d + d2a Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!