If x, y and z are variables, verify the cyclic symmetry of the following expressions.
(1) x(y + z) + y(z + x) + z(x + y)
(2) xy(x − y) + yz(y − z) + zx(z − x)
(3) x2y(x + y) + y2z(y + z) + z2x(z + x)
(4) x3(x + y) + y3(y + z) + z3(z + x)
(5) xy2(x − y) + yz2(y − z) + zx2(z − x)
If x, y and z are variables, verify the cyclic symmetry of the following expressions.
(1) x(y + z) + y(z + x) + z(x + y)
(2) xy(x − y) + yz(y − z) + zx(z − x)
(3) x2y(x + y) + y2z(y + z) + z2x(z + x)
(4) x3(x + y) + y3(y + z) + z3(z + x)
(5) xy2(x − y) + yz2(y − z) + zx2(z − x)
(1) The given expression is 
... (1)
Changing the variables x, y and z cyclically, we get 
... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression 
is a cyclic symmetrical expression
(2) The given expression is 
... (1)
Changing the variables x, y and z cyclically, we get 
... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression 
is a cyclic symmetrical expression
(3) The given expression is 
... (1)
Changing the variables x, y and z cyclically, we get 
... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression 
is a cyclic symmetrical expression.
(4) The given expression is 
... (1)
Changing the variables x, y and z cyclically, we get 
... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression 
is a cyclic symmetrical expression
(5) The given expression is 
... (1)
Changing the variables x, y and z cyclically, we get 
... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression 
is a cyclic symmetrical expression
(1) The given expression is ... (1)
Changing the variables x, y and z cyclically, we get ... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression is a cyclic symmetrical expression
(2) The given expression is ... (1)
Changing the variables x, y and z cyclically, we get ... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression is a cyclic symmetrical expression
(3) The given expression is ... (1)
Changing the variables x, y and z cyclically, we get ... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression is a cyclic symmetrical expression.
(4) The given expression is ... (1)
Changing the variables x, y and z cyclically, we get ... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression is a cyclic symmetrical expression
(5) The given expression is ... (1)
Changing the variables x, y and z cyclically, we get ... (2)
Comparing expressions (1) and (2), we observe that they are same.
Hence, the expression is a cyclic symmetrical expression
