Show that `|b c-a^2c a-b^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c a-b^2|=|a^2c^2 2a c-b^2 2a b-c^2b^2a^2b^2 2b c-a^2c^2|`

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

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

Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(a-b)^2, ab]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

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

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

Prove that |[(b+c)^2, a^2, bc],[(c+a)^2, b^2, ca],[(a+b)^2, c^2, ab]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[ c^2,c^2-(a-b)^2,a b]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)