Using properties of determinants, prove the following : `|b+c a a b c+a b cc a+b|=4a b c`

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

Prove: |b+c a a b c+a b cc a+b|=4a b c

Prove that |b+c a a b c+a b cc a+b|=4a b c

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)

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 the following : det[[a,a^(2),bcb,b^(2),cac,c^(2),ab]]=(a-b)(b-c)(c-a)(bc+ca+ab)

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3

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

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)