Question

Calculati: (X+2) la puterea a 2- a - (minus) (x+3)(x-3) + (2x-1) la puterea a 2-a.

Answer 1

$(x+2)^2-(x+3)(x-3)+(2x-1)^2= \\ =x^2+2\cdot x\cdot 2+2^2-x^2-3^2+(2x)^2=2\cdot 2x \cdot 1+1^2=\\ =x^2+4x+4-x^2-9+4x^2-4x+1=\\=4x+4-9+4x^2-4x+1= \\ =4-9+4x^2+1= \\ =-5+4x^2+1=-4+4x^2=4x^2-4=2^2x^2-2^2=(2x)^2-2^2= \\ =\bold{(2x-2)(2x+2)};$