Znajdź jak najprostszą postać wyrażenia : (x+1)(x^99 - x^98 + x^97 - ... - x^2 + x -1) Pomocy . ! Pilne ... na jutro :/

[latex](x+1)(x^{99}-x^{98}+x^{97}-..-x^2+x-1)=\ =(x+1)(x-1+x^3-x^2+x^5-x^4+...+...x^{99}-x^{98})=\ =(x+1)(x-1)(1+x^2+x^4+x^6+...+x^{96}+x^{98})=\ =(x+1)(x-1)(1+x^2)underbrace{(1+x^4+x^8+...+x^{92}+x^{96})}_{n=25 a_1=1 q=x^4}=\ =(x^2-1)(x^2+1)( frac{1-x^{100}}{1-x^4})=(x^4-1)( frac{x^{100}-1}{x^4-1})=\ x^{100}-1[/latex] [latex] oindent ule[0.5cm]{ extwidth}{1pt}[/latex] ///Khan.