Outra de fatoração

Fatore (a+b+c)³ -a³ - b³ - c³.

(a+b+c)² = a² + b² + c² + 2(ab+ac + bc)
(a+b+c)³ = (a+b+c) [ a² + b² + c² + 2(ab+ac + bc) ]

(a+b+c)³ = a³ + b³ + c³ + 3ab² + 3ac² + 3ba² + 3bc² + 3ca² + 3cb² + 6 abc
(a+b+c)³ -a³-b³-c³ = 3ab² + 3ac² + 3ba² + 3bc² + 3ca² + 3cb² + 6 abc
X = 3(ab² + ac² + ba² + bc² + ca² + cb² + 2abc)
X = 3( ab(a+b) + ac(a+c) + bc(b+c) + 2abc)
X = 3( ab(a+b) + abc + ac(a+c) + abc + bc(b+c) )
X = 3( ab(a+b+c) + ac(a+b+c) + bc(b+c) )
X = 3( (a+b+c)(ab+ ac) + bc(b+c) )
X = 3( a(a+b+c)(b+c) + bc(b+c) )
X = 3( (b+c)( a(a+b+c) + bc )
X = 3( (b+c) (a² + ab + ac + bc )
X = 3( (b+c) (a(a+b) + c(a+b) )
X = 3(b+c)(a+b)(a+c)