Using binomial theorem, evaluate: (102)5 - Vidyadip

Question

Using binomial theorem, evaluate: (102)⁵

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Answer

(102)⁵ = (100 + 2)⁵
Using binomial theorem, we have
${(100 + 2)^5}{ = ^5}{C_0}{(100)^5}{ + ^5}{C_1}{(100)^4}(2)$${ + ^5}{C_2}{(100)^3}{(2)^2}$
${ + ^5}{C_3}{(100)^2}{(2)^3}{ + ^5}{C_4}(100){(2)^4}$${ + ^5}{C_5}{(2)^5}$
= (100)⁵ + 5(100)⁴(2) + 10(100)³(2)² + 10(100)²(2)³ + 5(100)(2)⁴ + (2)⁵
= 10000000000 + 1000000000+ 40000000 + 800000 + 8000 + 32
= 11040808032

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