Show that |a b c a^2b^2c^2b cc a a b|=|1...

Show that `|a b c a^2b^2c^2b cc a a b|=|1 1 1a^2b^2c^2a^2b^2c^3|=(a-b)(b-c)(c-a)(a b+b c+c a)` .

A

(a-b)(b-c)(c-a)

B

(a-b)(b-c)(c-a)(a+b+c)

C

(a-b)(b-c)(c-a)(ab+bc+ca)

D

(a-b)(b-c)(c-a)abc

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c^2 .

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a(a+b+c)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-c)(c-a)

Prove that |{:(a,b,c),(a^(2),b^(2),c^(2)),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)