Factorize each of the following expressions:
(a-2b)3-512b3
Given,
(a – 2b)3 – 512b3
= (a – 2b)3 – (8b)3
= (a – 2b – 8b) {(a – 2b)2 +(8b)2 +(a – 2b) 8b}
= (a – 10b) (a2 +4b2 – 4ab +64b2 +8ab – 16b2)
= (a – 10b) (a2 +52b2 +4ab)