Question
Expand $(3 x-y)^{4}$
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Answer
$(3 x-y)^{4}=[3 x+(-y)]^{4}$
$={ }^{4} \mathrm{C}_{0}(3 x)^{4}(-y)^{0}+{ }^{4} \mathrm{C}_{1}(3 x)^{3}(-y)^{1}+{ }^{4} \mathrm{C}_{2}(3 x)^{2}(-y)^{2}+{ }^{4} \mathrm{C}_{3}(3 x)^{1}(-y)^{3}+{ }^{4} \mathrm{C}_{4}(3 x)^{0}(-y)^{4}$
$=81 x^{4}+4\left(27 x^{3}\right)(-y)+6\left(9 x^{2}\right)\left(y^{2}\right)+4(3 x)\left(-y^{3}\right)+y^{4}$
$=81 x^{4}-108 x^{3} y+54 x^{2} y^{2}-12 x y^{3}+y^{4}$
$={ }^{4} \mathrm{C}_{0}(3 x)^{4}(-y)^{0}+{ }^{4} \mathrm{C}_{1}(3 x)^{3}(-y)^{1}+{ }^{4} \mathrm{C}_{2}(3 x)^{2}(-y)^{2}+{ }^{4} \mathrm{C}_{3}(3 x)^{1}(-y)^{3}+{ }^{4} \mathrm{C}_{4}(3 x)^{0}(-y)^{4}$
$=81 x^{4}+4\left(27 x^{3}\right)(-y)+6\left(9 x^{2}\right)\left(y^{2}\right)+4(3 x)\left(-y^{3}\right)+y^{4}$
$=81 x^{4}-108 x^{3} y+54 x^{2} y^{2}-12 x y^{3}+y^{4}$
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