Using properties of determinants, show that `|(b+a,a,a),(b,c+a,b),(c,c,a+b)|=4abc`

Using properties of determinant show that |(a+b,a,b),(a,a+c,c),(b,c,b+c)|=4abc

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)

Using properties of determinants, Find |(b+c,a,a),(b,c+a,b),(c,c,a+b)|

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

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)

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)