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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem3 Marks
Question
Evaluate the following:
$(\sqrt3+1)^5-(\sqrt3-1)^5$
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Answer

$(\sqrt3+1)^5-(\sqrt3-1)^5$
$=2\big[{^5\text{C}}_1(\sqrt3)^4+{^5\text{C}}_3(\sqrt3)^2+{^5\text{C}}_5\big]$
$=2\big[5\times9+10\times3+1\big]$
$=2\big[45+30+1\big]$
$=2\big[76\big]$
$=152$

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