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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

\frac{- x ^{2} + 14 x - 36}{( x ^{2} - 36 ) ^{2}}

\frac{1}{s ( s ^{2} + x )}

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

\frac{5 ( x - 2 )}{2}

\frac{18 x ^{3}}{( x - 0.5 ) ( x - 0.8 ) ^{2}}

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