Question

Using factor theorem , show that (a-b)is the factor of a (b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)
Pls anyone who gives ans i will give points

Answer 1

Step-by-step explanation:

a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)

=ab^2-ac^2+bc^2-ba^2+ca^2-cb^2

=ab^2-ac^2+bc^2-ba^2+ca^2-cb^2+abc-abc

=abc-ba^2-ac^2+ca^2-cb^2+ab^2+bc^2-abc

=ab(c-a)-ac(c-a)-b^2(c-a)+bc(c-a)

=(ab-ac-b^2+bc)(c-a)

={a(b-c)-b(b-c)}(c-a)

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