Solve $(a + b + c)^{3}$

Question

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Answer 1

$(a + b + c) ³ = (a ³ + 3 a ² b + 3 a b ² + b ³) + 3 (a ² + 2 a b + b ²) c + 3 (a + b) c 2 + c ³$

$(a + b + c) ³ = a ³ + b ³ + c ³ + 3 a ² b + 3 a ² c + 3 a b ² + 3 b ² c + 3 a c ² + 3 b c ² + 6 a b c$

$(a + b + c) ³ = (a ³ + b ³ + c ³) + (3 a ² b + 3 a ² c + 3 a b c) + (3 a b ² + 3 b ² c + 3 a b c) + (3 a c ² + 3 b c ² + 3 a b c) - 3 a b c$

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

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

$(a + b + c) ³ = (a ³ + b ³ + c ³) + 3 [(a + b + c) (a b + a c + b c) - a b c]$

Answer 2

(a + b + c) ³ = (a ³ + 3 a ² b + 3 a b ² + b ³) + 3 (a ² + 2 a b + b ²) c + 3 (a + b) c 2 + c ³

(a + b + c) ³ = a ³ + b ³ + c ³ + 3 a ² b + 3 a ² c + 3 a b ² + 3 b ² c + 3 a c ² + 3 b c ² + 6 a b c

(a + b + c) ³ = (a ³ + b ³ + c ³) + (3 a ² b + 3 a ² c + 3 a b c) + (3 a b ² + 3 b ² c + 3 a b c) + (3 a c ² + 3 b c ² + 3 a b c) - 3 a b c

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

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

(a + b + c) ³ = (a ³ + b ³ + c ³) + 3 [(a + b + c) (a b + a c + b c) - a b c]