What is expand (θ+αθ^2-α^2θ^3)/((1-αθ)^3) ?

The solution to expand (θ+αθ^2-α^2θ^3)/((1-αθ)^3) is (θ+θ^2α-θ^3α^2)/(1-3θα+3θ^2α^2-θ^3α^3)

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expand (θ+αθ^2-α^2θ^3)/((1-αθ)^3)

expand

\frac{θ + α θ ^{2} - α ^{2} θ ^{3}}{( 1 - α θ ) ^{3}}

\frac{θ + θ ^{2} α - θ ^{3} α ^{2}}{1 - 3 θ α + 3 θ ^{2} α ^{2} - θ ^{3} α ^{3}}

Solution steps

\frac{θ + α θ ^{2} - α ^{2} θ ^{3}}{( 1 - α θ ) ^{3}}

(1 - α θ)^{3} = 1 - 3 θ α + 3 θ^{2} α^{2} - θ^{3} α^{3}

= \frac{θ + θ ^{2} α - θ ^{3} α ^{2}}{1 - 3 θ α + 3 θ ^{2} α ^{2} - θ ^{3} α ^{3}}

\frac{2 l ( ( - 1 ) ^{n} - 1 )}{π ^{2} n ^{2}}

y + \frac{x}{2} + \frac{3}{2}

4 r^{2} - r^{2} (33 - π)

b (a + b + c)^{3}

(x e^{x}) (1 + e^{x})

What is expand (θ+αθ^2-α^2θ^3)/((1-αθ)^3) ?
The solution to expand (θ+αθ^2-α^2θ^3)/((1-αθ)^3) is (θ+θ^2α-θ^3α^2)/(1-3θα+3θ^2α^2-θ^3α^3)