Question

The simplest form of the expression $ab(a-b)+bc(b-c)+ca(c-a)$ is?

• A. $a^2(b-c)-a(b+c)(b-c)+bc(b-c)$
• B. $(a-b)(b-c)(c-a)$
• C. $-(a-b)(b-c)(c-a)$
• D. $(b-c)(a^2-ab-ac+bc)$

Answer 1

The correct option is C $-(a-b)(b-c)(c-a)$

Given expression is $ab(a-b)+bc(b-c)+ca(c-a)$

Taking out $b$ common from the first two terms, we have

$b(a^2-ab+cb-c^2)+ca(c-a)$

$=b^2(c-a)-(a+c)(c-a)+ca(c-a)$

$=(c-a)(b^2-a-c+ca)$

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

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