Using binomial theorem, evaluate: (101)4 - Vidyadip

Question

Using binomial theorem, evaluate: (101)⁴

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Answer

(101)⁴ = (100 + 1)⁴
Using binomial theorem, we have
${(100 + 1)^4}{ = ^4}{C_0}{(100)^4}{ + ^4}{C_1}{(100)^3}(1)$${ + ^4}{C_2}{(100)^2}{(1)^2}{ + ^4}{C_3}(100){(1)^3}{ + ^4}{C_4}{(1)^4}$
= (100)⁴ + 4(100)³ + 6(100)² + 4(100) + 1
= 100000000 + 4000000 + 60000 + 400 + 1
= 104060401

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