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Let f(a) = (a + b + c)³ - (a³+b³+c³)
Put a = – b in f(a), we get
f(– b) = ( – b + b + c)³ – [(– b )³+b³+c³]
= c³ – [– b³ + b³ + c³]
= c³ – c³
∴ f(– b) = 0
Hence (a + b) is a factor of [(a + b + c)³ - (a³+b³+c³)]
Similarly, we can prove (b + c) and (c + a) are factors of [(a + b + c)³ - (a³+b³+c³)].
:) Hope this helps!!!!
Put a = – b in f(a), we get
f(– b) = ( – b + b + c)³ – [(– b )³+b³+c³]
= c³ – [– b³ + b³ + c³]
= c³ – c³
∴ f(– b) = 0
Hence (a + b) is a factor of [(a + b + c)³ - (a³+b³+c³)]
Similarly, we can prove (b + c) and (c + a) are factors of [(a + b + c)³ - (a³+b³+c³)].
:) Hope this helps!!!!
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