Binomial Theorem

I have calculated myself on the top line.
Sorry!

Hello Max!

$\text{What's } (x+\frac{1}{x})^4 \text{ ?}$ 

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

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

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

Greeting asinus :- )

   !