What is expand (2x+y)*(x+y/x)^5 ?

The solution to expand (2x+y)*(x+y/x)^5 is (2(x^2+y)^5)/(x^4)+((x^2+y)^5y)/(x^5)

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expand (2x+y)*(x+y/x)^5

expand

(2 x + y) \cdot (x + \frac{y}{x})^{5}

\frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

Solution steps

(2 x + y) (x + \frac{y}{x})^{5}

= (x + \frac{y}{x})^{5} (2 x + y)

Apply the distributive law:

a (b + c) = ab + a c

(x + \frac{y}{x})^{5} (2 x + y) = (x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y

= (x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y

Simplify

(x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y : \frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

= \frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

(x^{- 2})^{2}

\frac{( 3 x - 11 ) ^{2}}{64}

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

A (3, 2, - 4) B (- 5, 4, 4)

What is expand (2x+y)*(x+y/x)^5 ?
The solution to expand (2x+y)*(x+y/x)^5 is (2(x^2+y)^5)/(x^4)+((x^2+y)^5y)/(x^5)