Verify the cyclic symmetry of the following expressions if a, b and c

1.	Verify the cyclic symmetry of the following expressions if a, b and c are the variables:(1) a(b − c) + b(c − a) + c(a − b)(2) ab(a + b) + bc(b + c) + ca(c + a)(3) a2b(a − b) + b2c(b − c) + c2a(c − a)(4) a2(a + b) + b2(b + c) + c2(c + a)(5) ab2(a − b) + bc2(b − c) + ca2(c − a)
Answer» Verify the cyclic symmetry of the following expressions if a, b and c are the variables: (1) a(b − c) + b(c − a) + c(a − b) (2) ab(a + b) + bc(b + c) + ca(c + a) (3) a²b(a − b) + b²c(b − c) + c²a(c − a) (4) a²(a + b) + b²(b + c) + c²(c + a) (5) ab²(a − b) + bc²(b − c) + ca²(c − a)

Verify the cyclic symmetry of the following expressions if a, b and c are the variables:(1) a(b − c) + b(c − a) + c(a − b)(2) ab(a + b) + bc(b + c) + ca(c + a)(3) a2b(a − b) + b2c(b − c) + c2a(c − a)(4) a2(a + b) + b2(b + c) + c2(c + a)(5) ab2(a − b) + bc2(b − c) + ca2(c − a)

Answer»

Verify the cyclic symmetry of the following expressions if a, b and c are the variables:

(1) a(b − c) + b(c − a) + c(a − b)

(2) ab(a + b) + bc(b + c) + ca(c + a)

(3) a²b(a − b) + b²c(b − c) + c²a(c − a)

(4) a²(a + b) + b²(b + c) + c²(c + a)

(5) ab²(a − b) + bc²(b − c) + ca²(c − a)

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Verify the cyclic symmetry of the following expressions if a, b and c are the variables:(1) a(b − c) + b(c − a) + c(a − b)(2) ab(a + b) + bc(b + c) + ca(c + a)(3) a2b(a − b) + b2c(b − c) + c2a(c − a)(4) a2(a + b) + b2(b + c) + c2(c + a)(5) ab2(a − b) + bc2(b − c) + ca2(c − a)

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