1)

[1bc+adb2c2+a2d21ca+bdc2a2+b2d21ab+cda2b2+c2d2]=


A) (a-b)(b-c)(c-d)(a-d)(a-c)(d-b)

B) (a-b)(a-c)(b-c)(b-d)(a-d)(c-d)

C) (a-b)(a-c)(a-d)(b-c)(b-d)(d-c)

D) (a-b)(b-c)(c-d((b-d)

Answer:

Option B

Explanation:

|111bc+adca+bdab+cdb2c2+a2d2c2a2+b2d2a2b2+c2d2|

 Applying c1c1c2  and  c2=c2c3

|001c(ba)+d(ab)c(ad)+b(da)ab+cdc2(b2a2)+d2(a2b2)c2(a2d2)+b2(d2a2)a2b2+c2d2|

1[{c(ba)+d(ab)}{c2(a2d2)+b2(d2a2)}

[{c(ad)+b(da)}{c2(b2a2)+d2(a2b2)}]

 often after simplify we are getting

  (a-b)(a-c)(b-c)(b-d)(a-d)(c-d)