The value of determinant ( | array ccc a-b & b+c & a b-a & c+a & b c-a & a+b & c array | ) is

Step-by-step solution

Given that, ( | array ccc a-b & b+c & a b-c & c+a & b c-a & a+b & c array | ) ( C₃ C₂+C₃ ) ( | array lll a-b & b+c & a+b+c b-c & c+a & a+b+c c-a & a+b & a+b+c array | ) ( =a+b+c) | array ccc a-b & b+c & 1 b-c & c+a & 1 c-a & a+b & 1 array | ) ( =(a+b+c)((c+a)(c-a)-(a+b)(b-c) ) ( -(b+c)(c-a)-(a+b)(a-b) ) ( +(b+c)(b-c)-(c+a)(a-b)) ) ( =(a+b+c) (c²-a²-a b+a c-b²+b c ) ) ( -b c+a b-c²+a c-a²+b² ) ( .+b²-c²-a c+b c-a²+a b ) ) ( =(a+b+c) (-c²-3 a²+a b+a c+b²+b c ) ) ( =a (-c²-3 a²+a b+a c+b²+b c ) ) ( +b (-c²-3 a²+a b+a