Question

Using Binomial Theorem, evaluate \((101)^4\)

Answer 1

\(101\) 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, \(101 = 100 + 1\)
\((101)^4 = (100+1)^4\)
=\(^4C_0(100)^4 +^4C_1(100)^3(1)+^4C_2(100)^2(1)^2 + ^4C_3(100)(1)^3 + ^4C_4(1)^4\)
=\((100)^4+4(100)^3+6(100)^2+4(100)+(1)^4 \)
=\(100000000+4000000+60000+400+1\)
=\(104060401\)