Question

the value of 997 to the power 1 by 3 according to Binomial Theorem is

Answer 1

The binomial theorem states that (a+b)n=n∑k=0(nk)an−kbk

where (nk)=n!k!(n−k)!

For this problem, we will only need to calculate for n=3, and we will find that (30)=(33)=1 and (31)=(32)=3
(Try verifying this)

Noting that it is much easier to calculate powers of 10 and 1 compared to 999, we can rewrite 999as 1000−1=103−1 and apply the binomial theorem:

9993=(103−1)3

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