Evaluate: (i)(x^2+x+1)(x^2-x+1) (ii) (a-b+c)(b+c-a) (iii) (a+b+c) (a+b-c)
(i) (x2+x+1)(x2-x+1)
=x2(x2-x+1)+x(x2-x+1)+1(x2-x+1)
= x4 -x3 +x2 +x3-x2+x+x2-x+1
= x4+x2+1
(ii) (a-b+c)(b+c-a)
= (c+a-b)(c-a+b)
={c+(a-b)}{c-(a-b)}
= c2 -(a-b)2
= c2 -(a2-2ab+b2)
= c2-a2+2ab+b2
(iii) (a+b+c) (a+b-c)
={(a+b)+c)}{(a+b)-c)}
= (a+b)2 -c2
=a2+2ab+b2-c2
= a2+b2-c2+2ab