Question

Descompunerea in produs de factori expresia
a^{2} b+a b^{2} +2ab+ a^{2} +b^{2} +a+b[/tex]

Answer 1

a²b + ab² + 2ab + a² + b² + a +b = 
= (a²b +  ab²)  + (a + b )+ ( 2ab + a² +b² ) = 
= ab( a +b) + ( a+ b) + ( a +b)²
= ( a + b) ( ab +  1 + a +b ) 
= ( a +b ) [ ( ab + a) + ( 1 +b) ] 
= ( a +b) [a( b +1)  + ( 1 +b) ] =
= ( a + b) · ( b +1) ·( a + 1)

Answer 2

a² b + a b² + 2ab + a² + b² + a + b =
= ab (a + b) + (a + b)² + (a + b) =
= (a + b) [(ab) + (a + b) + 1] =
= (a + b) (ab + a + b + 1) =
= (a + b) [a (b + 1) + (b + 1)] =
= (a + b) (a + 1) (b + 1)