Expand the following:-
(A) (a-3b+c)^2
(B) (a+b-c)^2-(a-b+c)^2
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(A).(a-3b+c)²
= a²+(-3b)²+c²+2(a)(-3b)+2(-3b)(c) +2ca
=a²+9b²+c²-6ab-6bc+2ca
(B).(a+b-c)²-(a-b+c)²
= a²+b²+(-c)²+2ab+2b(-c)+2(-c)a - [a²+(-b)²+c²+2a(-b)+2(-b)c+2ca]
= a²+b²+c²+2ab-2bc-2ca-a²-b²-c²+2ab+2bc-2ca
= 4ab-4ca
= 4a(b-c)
= a²+(-3b)²+c²+2(a)(-3b)+2(-3b)(c) +2ca
=a²+9b²+c²-6ab-6bc+2ca
(B).(a+b-c)²-(a-b+c)²
= a²+b²+(-c)²+2ab+2b(-c)+2(-c)a - [a²+(-b)²+c²+2a(-b)+2(-b)c+2ca]
= a²+b²+c²+2ab-2bc-2ca-a²-b²-c²+2ab+2bc-2ca
= 4ab-4ca
= 4a(b-c)
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