Question

Using factor theorem, Show that (a - b) is the factor of a (b²- c²) +b (c²-a²) + c (a²-b²) Answer Plzzz

Answer 1

Answer:

a(b²-c²)+b(c²-a²)+c(a²-b²)

=ab²-ac²+bc²-a²b+a²c-b²c

=ab²-a²b-ac²+bc²+a²c-b²c

=ab(b-a)-c²(a-b)+c(a²-b²)

=-ab(a-b)-c²(a-b)+c((a+b)(a-b))

=(a-b)[-ab-c²+c(a+b)]

=(a-b)[-ab+cb-c²+ac]

=(a-b)[-b(c-a)-c(c-a)]

=(a-b)(b-c)(c-a)

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