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) (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}}

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

A (8, 2) B (3, - 4)

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

b cs in (b + c) (cot (b) + cot (c))

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)