Find the value of : `|(b+c,a,a),(b,c+a,b),(c,c,a+b)|`

Find the value of : |(1,a, b+c),(1 , b, c+a),(1,c,a+b)|

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

Without expanding at any stage, find the value of |(0,a,-b),(-a,0,c),(b,-c,0)| .

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

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)|

What is the value of following determinant ? |(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|

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)

Prove that |(3a, -a+b, -a+c),(a-b, 3b, c-b),(a-c, b-c, 3c)| = 3(a+b+c)(ab+bc+ca) .