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

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

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

Using the properties of determinants,prove that ollowing det[[a-b,-c^(2),a^(2)a^(2),-c,-a^(2)b^(2),c^(2),-a-b]]=(a+b+c)^(3)

Using the properties of determinants, prove the following |{:((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 the properties of determinants, prove the following |{:(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(a-1)^2,(c-1)^2):}|=4|{:(a^2,b^2,c^2),(a,b,c),(1,1,1):}|

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

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

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

Using the properties of determinants, prove the following |{:((a+b)^2,ca,cb),(ca,(b+c)^2,ab),(bc,ab,(c+a)^2):}|=2abc(a+b+c)^3