Question

Ma puteti ajuta la descompunerea (x+y)(x+y+2)+1?

Answer 1

   
[tex]\displaystyle\\ (x+y)(x+y+2)+1 =\\ \\ =(x+y)[(x+y)+2]+1= \\ \\ =(x+y)^2 + 2(x+y) + 1 =~~~~\text{Notatie: a = (x+y)}\\\\ =a^2 + 2a + 1=\\\\ =a^2 + a + a +1=\\\\ =a(a+1)+a+1 = ~~~~~\text{Dam factor comun pe a+1}\\\\ =(a+1)(a+1) = (a+1)^2=\boxed{(x+y+1)^2} ~~~~~~\text{Deoarece a = x+y}[/tex]