Question

factories (a-b)^3+(b-c)^3+(c-a)^3​

Answer 1

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(a-b)3+(b-c)3+(c-a)3

= a3 - b3 - 3×a2×b + 3×a×b2 + b3 -c3 -3 × b2 × c + 3×b×c2 + c3 -b3 - 3×c2×b

= -3×a2×b + 3×a×b2 - 3×b2×c + 3×b×c2 - 3×c2×a + 3×c×a2

=3×[ab(b-a) + bc(c-b) + ca(a-c) ]

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