Factorize each of the following:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(i) Using identity,
(a + b)3 = a3 + b3 + 3a2b + 3ab2
8a3 + b3 + 12a2b + 6ab2
= (2a)3 + b3 + 3 (2a) (2b) + 3 (2a) (b)2
= (2a + b)3
= (2a + b) (2a + b) (2a + b)
(ii) Using identity,
(a + b)3 = a3 + b3 + 3a2b + 3ab2
8a3 – b3 – 12a2b + 6ab2
= (2a)3 – b3 – 3 (2a)2b + 3 (2a) (b)2
= (2a – b)3
= (2a – b) (2a – b) (2a – b)
(iii) Using identity,
(a + b)3 = a3 + b3 + 3a2b + 3ab2
27 – 125a3 – 135a + 225a2
= 33 – (5a)3 – 3 (3)2(5a) + 3 (3) (5a)2
= (3 – 5a)3
= (3 – 5a) (3 – 5a) (3 – 5a)
(iv) Using identity,
(a + b)3 = a3 + b3 + 3a2b + 3ab2
64a3 – 27b3 – 144a2b + 108ab2
= (4a)3 – (3b)3 – 3 (4a)2 (3b) + 3 (4a) (3b)2
= (4a – 3b)2
= (4a – 3b) (4a – 3b) (4a – 3b)
(v) Using identity,
(a + b)3 = a3 + b3 + 3a2b + 3ab2
27p3 - 
- 
p2 + 
p
= (3p)3 – (
)3 – 3 (3p)2 (
) + 3 (3p) (
)2
= (3p - 
)3
= (3p - 
) (3p - 
) (3p - 
)