Prove the identities: `|a^2a^2(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a b|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)`

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)

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

The determinant |a2\ a^2-(b-c)^2b c b^2b^2-(c-a)^2c a c^2c^2-(a-b)^2a b| is divisible by- a. a+b+c b. (a+b)(b+c)(c+a) c. a^2+b^2+c^2 d. (a-b)(b-c)(c-a)

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)

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

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

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