Question

Using binomial theorem, evaluate each of the following:
(101)^4​

Answer 1

Answer:

101 can be expressed as the sum or difference of two numbers whose powers are easier

to calculate and then, Binomial Theorem can be applied.

It can be written that, 101 = 100 + 1

Now, (101)4 = (100 + 1)4

= 4C0 (100)4 + 4C1 (100)3 (1) + 4C2 (100)2(1)2 + 4C3 (100) (1)3 + 4C4 (1)4

= (100)4 + 4(100)3 + 6(100)2 + 4(100) + 1

= 100000000 + 4000000 + 60000 + 400 + 1

= 104060401