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(a+b+c)³ = a³+b³+c³ +3(a+b)(b+c)(a+c)
inlocuiesc pe (a+b+c)³ in ecuatia data
⇒a³+b³+c³ = a³+b³+c³ +3(a+b)(b+c)(a+c) - 3(a+b)(b+c)(a+c)
⇒a³+b³+c³ = a³+b³+c³