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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem2 Marks
Question
Using binomial theorem, evaluate: $(96)^3$
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Answer

$(96)^3 = (100 - 4)^3$
Using binomial theorem, we have
$(100 - 4)^3 =\ ^3C_0(100)^3 +\ ^3C_1(100)^2 (-4) +\ ^3C_2(100)(-4)^2 +\ ^3C_3(-4)^3$
$= (100)^3 + 3.10000 (-4) + 3.100.16 + (-64)$
$= 1000000 - 120000 + 4800 - 64$
$= 1004800 - 120064 = 884736$

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