Evaluate: (i)(x^2+x+1)(x^2-x+1) (ii) (a-b+c)(b+c-a) (iii) (a+b+c) (a+b-c)

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

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