Question

pls help me with this question.
factorise the above sum. (with help of formula)​

Answer 1

$Given \: a^{2}(b-c)^{2} - b^{2}(c-a)^{2}$

$= [a(b-c)]^{2} - [b(c-a)]^{2}$

$= (ab-ac)^{2} - (bc-ab)^{2}$

/* By algebraic identity */

$\boxed{ \pink{ x^{2} - y^{2} = (x+y)(x-y) }}$

$= [ (ab-ac)+ (bc-ab)] [ (ab-ac)- (bc-ab)]$

$= (ab-ac+ bc-ab)(ab-ac- bc+ab)$

$= (-ac +bc) ( 2ab - ac - bc )$

$= c(b-a)(2ab - ac - bc )$

Therefore.,

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

$\green {= c(b-a)(2ab - ac - bc ) }$

•••♪