What is expand (x^3(x-1)^2)/((2x+1)^2) ?

The solution to expand (x^3(x-1)^2)/((2x+1)^2) is (x^5-2x^4+x^3)/(4x^2+4x+1)

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expand (x^3(x-1)^2)/((2x+1)^2)

expand

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

\frac{x ^{5} - 2 x ^{4} + x ^{3}}{4 x ^{2} + 4 x + 1}

Solution steps

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

(2 x + 1)^{2} = 4 x^{2} + 4 x + 1

= \frac{x ^{3} ( x - 1 ) ^{2}}{4 x ^{2} + 4 x + 1}

(x - 1)^{2} = x^{2} - 2 x + 1

= \frac{x ^{3} ( x ^{2} - 2 x + 1 )}{4 x ^{2} + 4 x + 1}

Expand

x^{3} (x^{2} - 2 x + 1) : x^{5} - 2 x^{4} + x^{3}

= \frac{x ^{5} - 2 x ^{4} + x ^{3}}{4 x ^{2} + 4 x + 1}

(cos (t) + cos (2 t))^{2}

(e^{i x} + e^{- i x})^{4}

ln (1 + 2 x) + (e^{2 x - x^{2}} - 1) 3 x + 1

\frac{sin ^{2} ( a ) ( 1 + cos ( a ) )}{1 - cos ( a )}

x^{4} (5 - x^{2}) d x

What is expand (x^3(x-1)^2)/((2x+1)^2) ?
The solution to expand (x^3(x-1)^2)/((2x+1)^2) is (x^5-2x^4+x^3)/(4x^2+4x+1)