Question

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

Cu factor comun

VA ROG

cu tot cu rezolvare

Repede

Answer 1

$(a + b) \times (b + c) \times (c + a) - (a + b) \times (b - c) \times (a + c) = \\ \\ (a + b) \times (b + c) \times (a + c) - (a + b) \times (b - c) \times (a + c) = \\ \\ {a}^{2}b + abc + {a}^{2}c + {ac}^{2} + {b}^{2}a + {b}^{2}c + bca + {bc}^{2} - {a}^{2}b - abc + {a}^{2}c + {ac}^{2} - {b}^{2}a - {b}^{2}c + bca + {bc}^{2} = \\ \\ ( {a}^{2}b - {a}^{2}b) + (abc + abc - abc + abc) + ( {a}^{2}c + {a}^{2}c) + ( {ac}^{2} + {ac}^{2}) + ( {b}^{2}a - {b}^{2}a) + ( {b}^{2}c - {b}^{2}c) + ( {bc}^{2} + {bc}^{2}) = \\ \\ abc + abc + {2a}^{2}c + {2ac}^{2} + {2bc}^{2} = \\ \\ (abc + abc) + {2a}^{2}c + {2ac}^{2} + {2bc}^{2} = 2abc + {2a}^{2}c + {2ac}^{2} + {2bc}^{2}$