Question -
Answer -
(i) a4 – b4 – (a2)2 – (b2)2
[∵ a2 – b2 = (a – b)(a +b)]
= (a2 – b2) (a2 + b2)
= (a – b) (a + b) (a2 + b2)
(ii) p4 – 81 = (p2)2 – (9)2
= (p2 – 9) (p2 + 9)
[∵ a2 – b2 = (a – b)(a +b)]
= (p – 3)(p + 3) (p2 + 9)
(iii) x4 – (y + z)4 = (x2)2 – [(y + z)2]2
[∵ a2 – b2 = (a – b)(a +b)]
= [x2 – (y + z)2] [x2 + (y + z)2]
= [x – (y + z)] [x + (y + z)] [x2 + (y + z)2]
= (x – y – z) (x + y + z) [x2 + (y + z)2]
(iv) x4 – (x – z)4 = (x2)2 – [(y – z)2]2
= [x2 – (y – z)2] [x2 + (y – z)2]
= (x – y + z) (x + y – z) (x2 + (y – z)2]
(v) a4 – 2a2b2 + b4
= a4 – a2b2 – a2b2 + b4
= a2(a2 – b2) – b2(a2 – b2)
= (a2 – b2)(a2 – b2)
= (a2 – b2)2
= [(a – b) (a + b)]2
= (a – b)2 (a + b)2