F.2 Maths

(a﹣b+c)(a+b﹣c)

= [a﹣(b﹣c)] [a+(b﹣c)]

= a2﹣(b﹣c)2 【Using identity a2﹣b2=(a﹣b)(a+b)】

= a2﹣(b2﹣2bc + c2) 【Using identity (a﹣b)2=a2﹣2ab+b2】

= a2 ﹣b2 + 2bc﹣c2

= a2﹣b2﹣c2 + 2bc

a( a+b+c )-b( a+b+c )+c( a+b+c )
=a2+ab+ac-ab-b2-ac+ac+bc+c2
=a2-b2+c2+ab-ab+ac-ac+ac+bc
=a2-b2+c2+ac+bc

2007-11-12 19:54:09 補充：
=a2+ab+ac-ab-b2-bc+ac+bc+c2=a2-b2+c2+ab-ab+ac+ac-bc+bc=a2-b2+c2+2ac

(a-b+c) ( a+b+c )

=(a)2+ab+ac-ba-(b)2-bc+ca+cb+(c)2

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