produtos notáveis

a/(b+c)+b/(a+c)+c/(a+b)=
=(a∙(a+c)∙(a+b)+b∙(b+c)∙(a+b)+c∙(b+c)∙(a+c))/((b+c)∙(a+c)∙(a+b) )=
=((a^2+ac)∙(a+b)+(b^2+bc)∙(a+b)+(bc+c^2 )∙(a+c))/((ab+bc+ac+c^2 )∙(a+b) )=
=(a^3+a^2 b+a^2 c+abc+ab^2+b^3+abc+b^2 c+abc+bc^2+ac^2+c^3)/(a^2 b+ab^2+abc+b^2 c+a^2 c+abc+ac^2+bc^2 )=
=(a^3+b^3+c^3+a^2 b+a^2 c+ab^2+b^2 c+ac^2+bc^2+3abc)/(a^2 b+a^2 c+ab^2+b^2 c+ac^2+bc^2+2abc)=1

a^3+b^3+c^3+a^2 b+a^2 c+ab^2+b^2 c+ac^2+bc^2+3abc=
=a^2 b+a^2 c+ab^2+b^2 c+ac^2+bc^2+2abc

a^3+b^3+c^3+abc=0

a^3+b^3=-c^3-abc

a^2/(b+c)+b^2/(a+c)+c^2/(a+b)=
=(a^2∙(a+c)∙(a+b)+b^2∙(b+c)∙(a+b)+c^2∙(b+c)∙(a+c))/((b+c)∙(a+c)∙(a+b) )=
=((a+b)∙(a^3+a^2 c+b^3+b^2 c)+c^2∙(ab+bc+ac+c^2 ))/((b+c)∙(a+c)∙(a+b) )=
=((a+b)∙(-c^3-abc+a^2 c+b^2 c)+abc^2+bc^3+ac^3+c^4)/((b+c)∙(a+c)∙(a+b) )=
=(-ac^3-a^2 bc+a^3 c+ab^2 c-bc^3-ab^2 c+a^2 bc+b^3 c+abc^2+bc^3+ac^3+c^4)/((b+c)∙(a+c)∙(a+b) )=
=(a^3 c+b^3 c+abc^2+c^4)/((b+c)∙(a+c)∙(a+b) )=
=(c∙(a^3+b^3+abc+c^3 ))/((b+c)∙(a+c)∙(a+b) )=
=(c∙(0))/((b+c)∙(a+c)∙(a+b) )=0

Alternativa (A) 0.