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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Simplify

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

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

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

(x - 6)^{2}

\frac{2 x ^{2} - 3}{( x ^{2} - 9 ) ( x ^{2} - 4 )}

\frac{1}{s ( s - a ) ^{2}}

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

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