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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem2 Marks
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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