Question

using factor theorem show that a+b,b+c,c+a are factors of (a+b+c)^3-(a^3+b^3+c^3)

Answer 1

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)].

Answer 2

See attachment for the solution mate.

Hope it will help you.