Factorise : `|(1,1,1),(b+c,c+a,a+b),(b^2+c^2,c^2+a^2,a^2+b^2)|`

Factorise : |(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)|

Without expanding show that : |(bc,a,a^2),(ca,b,b^2),(ab,c,c^2)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

Using properties of determinant show that : |(a^2,bc,c^2+ac),(a^2+ab,b^2,ac),(ab,b^2+bc,c^2)|=4a^2b^2c^2

Using properties of determinant show that : |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Find the value of : |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|

Using properties of determinant show that : |(a,b+c,a^2),(b,c+a,b^2),(c,a+b,c^2)|=-(a+b+c)(a-b)(b-c)(c-a)

Without expanding show that : |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=2|(a,b,c),(b,c,a),(c,a,b)|

Without expanding show that : |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)|=0

Using properties of determinant show that : |(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b)|=(a+b+c)(a-b)(b-c)(c-a)