Question

Aratati ca (x+2)³ - x-2=(x+1)(x+2)(x+3) pentru orice x numar real.

Answer 1

(x+2)³ - (x+2)               = (x+1)(x+2)(x+3)
(x+2)[ (x+2)² - 1 ]         = (x+1)(x+2)(x+3)
(x+2)( x² + 4x + 4 - 1 ) = (x+1)(x+2)(x+3)
(x+2)( x² + 4x + 3 )       = (x+1)(x+2)(x+3)
(x+2)( x² + 3x + x + 3 ) = (x+1)(x+2)(x+3)
(x+2)[ x(x+3) + (x+3) ]  = (x+1)(x+2)(x+3)
(x+2)(x+3)(x+1)            = (x+1)(x+2)(x+3) , adevarat pentru orice x numar real.

Answer 2

dam factor comun in stanga pe (x+2)
(x+2)($x^{2} +4x+4-1$)=(x+2)($x^{2} +x+3x+3$)=(x+2)(x(x+1)+3(x+1))=
(x+2)(x+1)(x+2)