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Calculati: 
(x+x² -1)² 
Si formula daca se poate...


Răspuns :

(x+x² -1)²=(x(1+x)-1)^2= x^2(1+x)^2-2(x(1+x))+1=x^2(1+2x+x^2)-2x-2x^2+1=
=x^2+2x^3+x^4-2x-2x^2+1=x^4+2x^3-x^2+1=>

aplicand formula (a+b-c)^2=> a^2+2ab-2ac-2bc+b^2+c^2 =>
(x+x^2-1)^2 => x^2+2x^3-2x-2x^2+x^4+1