Evaluate using binomial theorem: (99)5.
(99)5 = (100 − 1)5
= 5C0(100)5 − 5C1(100)4(1) + 5C2(100)3(1)2 − 5C3(100)2(1)3 + 5C4(100)(1)4 − 5C5(1)5
= (100)5 − 5(100)4 + 10(100)3 − 10(100)2 + 5(100) − 1
= 10000000000 − 5000000000 + 1000000000 − 100000 + 500 − 1
= 9509900499
Answer: (99)5 = 9509900499