15. Using properties of determinants, prove the following `|[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|`=`a^3+b^3+c^3-3abc`

15.Using properties of determinants,prove the following b+c+aa+b

15.Using properties of determinants,prove the following det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc,]|=

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 the following |(3a,-a+b,-a+c),(a-b,3b,c-a),(a-c,b-c,3c)|=3(a+b+c)(ab+bc+ca)

Using properties of determinants,prove the b+c,a,ab,c+a,bc,c,a+b]|=4abc

det[[a,b,ca-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc

Using properties of determinants, prove 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)

|(1,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=a^(3)+b^(3)+c^(3)-3ab

5. Using the properties of determinants, prove 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]|

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