Using factor theorem, show that a-b, b-c, c-a are the factors of a(b2-c2) +b(c2-a2)\xa0+c(a2-b2).

Using factor theorem, show that a-b, b-c, c-a are the factors of a(b2-

1.	Using factor theorem, show that a-b, b-c, c-a are the factors of a(b2-c2) +b(c2-a2)\xa0+c(a2-b2).
Answer» If a - b is a factor of given expression, then a - b = 0 => a = bPutting a = b, in the given expression, we getb(b2-c2) +b(c2- b2) +c(b2- b2)= b3 - bc2 + bc2 - b3 + c(0)= 0Therefore, (a - b) is a factor of given expression.Again if (b - c) is a factor of given expression, thenPutting b - c = 0 => b = c in the given expression, we geta(c2 - c2) +c(c2 - a2) + c(a2 - c2)= a(0) + c3 - ca2 + ca2 - c3\xa0= 0Therefore, (b - c) is a factor of given expression.Again if (c - a) is a factor of given expression, thenPutting c - a = 0 => c = a in the given expression, we geta(b2 - a2) + b(a2 - a2) + a(a2 - b2)= ab2 - a3 + b(0) + a3 - ab2= 0Therefore, (c - a) is a factor of given expression