Question
Expand: $(2 x+3 y)^3$
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Answer
$(2 x+3 y)^3$
$={ }^3 C_0(2 x)^3(3 y)^0+{ }^3 C_1(2 x)^2(3 y)^1+{ }^3 C_2(2 x)(3 y)^2+{ }^3 C_3(2 x)^0(3 y)^3$
$=8 x^3+3\left(4 x^2\right)(3 y)+3(2 x)\left(9 y^2\right)+27 y^3$
$=8 x^3+36 x^3 y+54 x y^2+27 y^3$
$={ }^3 C_0(2 x)^3(3 y)^0+{ }^3 C_1(2 x)^2(3 y)^1+{ }^3 C_2(2 x)(3 y)^2+{ }^3 C_3(2 x)^0(3 y)^3$
$=8 x^3+3\left(4 x^2\right)(3 y)+3(2 x)\left(9 y^2\right)+27 y^3$
$=8 x^3+36 x^3 y+54 x y^2+27 y^3$
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