(i) [3-(a+b)][3+(a+b)] (ii) [4-(x+y)][4+(x+y)] (iii) (a-b)(a+b)(a^2+b^2)(a^4+b^4) [S.Chand Class 9 ICSE Exercise 3.1 Chapter 3 Expansion and Factorisation Solution]
(i) [3-(a+b)][3+(a+b)]
= (3)2 -(a+b)2 [∵ a2-b2=(a+b)(a-b)]
= 9 -(a2+2ab+b2)
= 9 -a2-2ab-b2
∴ [3-(a+b)][3+(a+b)] = 9 -a2-2ab-b2
(ii) [4-(x+y)][4+(x+y)]
= (4)2 -(x+y)2 [∵ a2-b2=(a+b)(a-b)]
=16-(x2+2xy+y2)
= 16-x2-2xy-y2
(iii) (a-b)(a+b)(a2+b2)(a4+b4)
= {(a-b)(a+b)}(a2+b2)(a4+b4)
= (a2-b2)(a2+b2)(a4+b4)
={ (a2-b2)(a2+b2)}(a4+b4)
={(a2)2-(b2)2}(a4+b4)
=(a4-b4)(a4+b4)
={(a4)2-(b4)2}
=a8-b8