a + b + c = 0, abc = - 15, aa (b + c) + bb (a + c) + cc (a + b)

a + b + c = 0, abc = - 15, aa (b + c) + bb (a + c) + cc (a + b)

∵ a + b + c = 0,
∴ a + b = - c b + c = - a + c = - b
∴ aa (b + c) + bb (a + c) + cc (a + b)
= - a & # 179; - b & # 179; - c & # 179;
= - a & # 179; - 3a & # 178; b - 3ab & # 178; - b & # 179; c & # 179; + 3a & # 178; b + 3ab & # 178;
= - (a + b) & # 179; - c & # 179; + 3a & # 178; b + 3ab & # 178;
= - (a + b + c) (a & # 178; + 2ab + b & # 178; + ac + bc + c & # 178;) + 3a & # 178; b + 3ab & # 178;
= - 0 * (a & # 178; + 2ab + b & # 178; + ac + bc + c & # 178;) + 3ab (a + b)
= 3ab * (- c)
= - 3abc
= - 3 * (- 15)
= 45