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

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

The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a) (a-b)(b-c)(c-a) (b) 3(a-b)(b-c)(c-a) (c) -3\ (a-b)(b-c)(c-a) (d) (a+b+c)(a^2+b^2+c^2-a b-b c-c a)

The value of the determinant |k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1| is k(a+b)(b+c)(c+a) k a b c(a^2+b^(f2)+c^2) k(a-b)(b-c)(c-a) k(a+b-c)(b+c-a)(c+a-b)

The value of the determinant |k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1| is k(a+b)(b+c)(c+a) k a b c(a^2+b^(f2)+c^2) k(a-b)(b-c)(c-a) k(a+b-c)(b+c-a)(c+a-b)

(a^(2)-b^(2)-2bc-c^(2))/(a^(2)+b^(2)+2ab-c^(2)) is equivalent to (a-b+c)/(a+b+c)( b) (a-b-c)/(a-b+c)(c)(a-b-c)/(a+b-c)(d)(a+b+c)/(a-b+c)

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

omega is an imaginary root of unity.Prove that (a+b omega+c omega^(2))^(3)+(a+b omega^(2)+c omega)^(3)=(2a-b-c)(2b-a-c)(2c-a-b)

The determinant |[a^2, a^2-(b-c)^2,bc],[b^2,b^2-(c-a)^2,ca],[ c^2,c^2-(a-b)^2,ab]| is divisible by- a. a+b+c b. (a+b)(b+c)(c+a) c. a^2b^2c^2 d. (a-b)(b-c)(c-a)