| array ccc 2 a & 2 b & b-c 2 b & 2 a & a+c a+b & a+b & b array | is divisible by -

Step-by-step solution

= | array ccc 2 a & 2 ~b & ~b - c 2 ~b & 2 a & a + c a + b & a + b & b array | aligned & R₂ R₂+R₁ & = | array ccc 2 a & 2 b & b-c 2(a+b) & 2(a+b) & a+b a+b & a+b & b array | & =(a+b) | array ccc 2 a & 2 b & b-c 2 & 2 & 1 a+b & a+b & b array | & C₁ C₁-C₂ & =(a+b) | array ccc 2(a-b) & 2 b & b-c 0 & 2 & 1 0 & a+b & b array | & =(a+b) 2(a-b)(2 b-a-b) & = & =2(a+b)(a-b)(b-a)=-2(a+b)(a-b)^2 . aligned