Question

Please factorize this equation
The answer is (a-b)(b-c)(c-a).

Answer 1

Follow-the-Steps :

First we need to check common factors in the polynomial,

so that we can factor out like ma+mb=m(a+b).

In case we miss some terms during the progress, express for a.

It adds simpleness to the polynomial.

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

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

common factor : b-c

$(b-c)\{a^2-a(b+c)+bc\}$

Now use a.c. method

$(b-c)\{(a-b)(a-c)\}$

Last, express in cyclic expression.

$\therefore(a-b)(b-c)(c-a)$