Question

Să se arate ca daca a,b,c aparține R, atunci: (a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a)

Answer 1

(a+b+c)³=a³+b³+c³+3a²b+3a²c+3ab²+3b²c+3ac²+3bc²+3abc=a³+b³+c³+3(a+b)(b+c)(a+c)

(a+b+c)³-a³-b³-c³=a³+b³+c³+3(a+b)(b+c)(a+c)-a³-b³-c³=3(a+b)(b+c)(a+c)

(a+b+c)³-a³-b³-c³=3(a+b)(b+c)(a+c) ,∀ a,b,c∈R