Find the value of: $(x + 2 y)^{9}$

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Solution

$(x + 2 y)^{9} =^{9} C_{0} x^{9} (2 y)^{0} +^{9} C_{1} x^{8} (2 y)^{1} +^{9} C_{2} x^{7} (2 y)^{2}$
$+^{9} c_{6} x^{3} (2 y)^{6} +^{9} c_{7} x^{2} (2 y)^{7} +^{9} c_{8} x^{1} (2 y)^{8}$
$+^{9} c_{9} x^{0} . (2 y)^{9}$
$(a + b)^{n} = \sum_{k = 0}^{n}^{n} c_{k} a^{n - k} . b^{k}$

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