prove that (a+b+c)^3-a^3-b^3-c^3=3(a+b)(b+c)(c+a).
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5
LHS= (a+b+c+)³-a³-b³-c³
= a³+b³+c³+3(a+b)(b+c)(c+a)-a³-b³-c³
= 3(a+b)(b+c)(c+a)
RHS= 3(a+b)(b+c)(c+a)
∴ LHS=RHS
= a³+b³+c³+3(a+b)(b+c)(c+a)-a³-b³-c³
= 3(a+b)(b+c)(c+a)
RHS= 3(a+b)(b+c)(c+a)
∴ LHS=RHS
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