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

The solution to expand (4x^4(1-x^2))/((1+x^2)^3) is (4x^4-4x^6)/(1+3x^2+3x^4+x^6)

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expand (4x^4(1-x^2))/((1+x^2)^3)

expand

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

\frac{4 x ^{4} - 4 x ^{6}}{1 + 3 x ^{2} + 3 x ^{4} + x ^{6}}

Solution steps

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

(1 + x^{2})^{3} = 1 + 3 x^{2} + 3 x^{4} + x^{6}

= \frac{4 x ^{4} ( - x ^{2} + 1 )}{1 + 3 x ^{2} + 3 x ^{4} + x ^{6}}

Expand

4 x^{4} (1 - x^{2}) : 4 x^{4} - 4 x^{6}

= \frac{4 x ^{4} - 4 x ^{6}}{1 + 3 x ^{2} + 3 x ^{4} + x ^{6}}

(1 - \frac{3}{3}) (1 + \frac{3}{3})

(5 + 1) (3 + 2)

\frac{1}{( s + 8 ) ( s ^{2} - 2 s + 2 )}

\frac{4 x ^{2} - 2 x + 1}{( x + 3 ) ^{3} ( x ^{2} - 7 ) ^{2}}

(1 + cos (x))^{2} + sin^{2} (x)

What is expand (4x^4(1-x^2))/((1+x^2)^3) ?
The solution to expand (4x^4(1-x^2))/((1+x^2)^3) is (4x^4-4x^6)/(1+3x^2+3x^4+x^6)