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

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

Using properties of determinants, prove that |{:(,a,b,b+c),(,c,a,c+a),(,b,c,a+b):}|=(a+b+c) (a-c)^2

Using properties of determinant, Show that |{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}|=2abc(a+b+c)^(3)

Using properties of determinants, prove that: |{:(a, a +b, a+b+c),(2a, 3a + 2b, 4a + 3b + 2c),(3a, 6a+3b, 10a + 6b + 3c):}| = a^(3)

Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)