Prove that det(a. b-c c+b

a+c. b c-a =(a+b+c)(a^2+b^2+c^2)

a-b b+a. c . )

Multiply c1 with a, c2 with b, c3 with c and then add all three columns, you will get a^2+b^2+c^2 in first column then take common and then r1->r1-r3 and r2->r2-r3 and then expand.