Factorise the expression.
`a ^(2) b + a^(2) c + ab + ac + b ^(2) c + c ^(2) b `

. Factorise the following expressions: i a^(2)+46a+205 iii) ab+ac-b^(2)-bcvi)a^(2)+b^(2)-2(ab-ac+bc)

. Factorise the following expressions: i a^(2)+46a+205 iii) ab+ac-b^(2)-bcvi)a^(2)+b^(2)-2(ab-ac+bc)

Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

Factorise: ab (c ^(2) +1) + c (a ^(2) + b ^(2))

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to