Question

# 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)

Solution

## (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 MathematicsMathematicsStandard X

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