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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