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High School Mathematics
6.19 Symmetric and Cyclic Expressions

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

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: x2 + y2 + z2, is this equation symmetry or not?

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

Q 3: Expand, a2b. (Variables 'a' and 'b')

Q 4: Simplify, (b-c)(b+c). (Variables a, b and c)

Q 5: Expand, a2b. (Variables a, b, c and d)
a2b +b2c + c2d
a2b +b2c + c2d + d2a
b2c + c2d + d2a
a2b + d2a

Q 6: Expand, (x + c). (Variables a, b and c)
(x + a) + (x + b) + (x + c)
(x + a)/(x + b)*(x + c)
(x + a)(x + b)
(x + a)(x + b)(x + c)

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