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Permutations , combinations and binomial expansion — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion2 Marks
Question
Expand $(3 a+2 y)^{3}$
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Answer

$(3 a+2 y)^{3}$
$={ }^{3} \mathrm{C}_{0}(3 a)^{3}(2 y)^{0}+{ }^{3} \mathrm{C}_{1}(3 a)^{2}(2 y)^{1}+{ }^{3} \mathrm{C}_{2}(3 a)^{1}(2 y)^{2}+{ }^{3} \mathrm{C}_{3}(3 a)^{0}(2 y)^{3}$
$=27 a^{3}+3\left(9 a^{2}\right)(2 y)+3(3 a)\left(4 y^{2}\right)+8 y^{3}$
$=27 a^{3}+54 a^{2} y+36 a y^{2}+8 y^{3}$

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