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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Simplify

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

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

(2 cos (2 x) cos (x) - cos (3 x)) sec (x^{\circ})

\frac{a}{12} \cdot \frac{9}{10}

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

(2 t + 2) (t - 32)

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

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