C₃→ C₂ + C₃ (i.e. replace 3^rd column by addition of 2^nd and 3^rd column)

Taking ab + bc + ac outside determinant

C₁→ C₁ - C₃ (i.e. replace 1^st column by subtraction of 1^st and 3^rd column)

If any one of the rows or columns of a determinant is 0 then the value of that determinant is 0.

∴ LHS = 0 = RHS

∴