Question

factorice (a + b) ^ 3 + (b + c) ^ 3 + (c + a) ^ 3 - 3(a + b) * (b + c) * (c + a)​

Answer 1

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Answer 2

$= (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac) \\ =(a + b + b + c + c + a) \binom{ {(a + b)}^{2} + {(b + c)}^{2} + {(c + a)}^{2} (a + b) (b + c) - (b + c)(c + a) - (a + b)(c + a)}{} \\ = 2(a + b + c)( {a}^{2} + {b}^{2} + 2ab + {b}^{2} + {c}^{2} + 2abc + {c}^{2} + {a}^{2} + 2ac - ab - ac - {b}^{2} - bc - bc - ab - {c}^{2} + ac - ac - bc - {a}^{2} - ab \\ = 2(a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - ac - bc) \\ = 2( {a}^{3} + {b}^{3} + {c}^{3} - 3abc$

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