[" 3.Prove that "(a+b+c)" is a factor of: "],[qquad |[a,b,c],[b,c,a],[c,a,b]|]

Show that a+b+c is a factor of |[a,b,c],[b,c,a],[c,a,b]|

Prove that (a+b+c+x) is a factor of |(x+a, b,c),(b,x+c,a),(c,a,x+b)|

Prove that |b+c a a b c+a b c c a+b |

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]|

Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]| . The other factor in the value of the determinant is

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a ,a+b, a+c],[ b+a,-2b,b+c],[c+a ,c+b,-2c]|. The other factor in the value of the determinant is

Using the factor theorem it is found that a+b , b+c and c+a are three factors of the determinant |[-2a, a+b ,a+c],[ b+a,-2b,b+c],[c+a, c+b, -2c]|dot The other factor in the value of the determinant is (a) 4 (b) 2 (c) a+b+c (d) none of these

Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+b^3+c^3-3a b c

Prove that '[[b-c,c-a,a-b],[b'-c'],[c'-a'][a'-b'],[b"-c",c"-a",a"-b"]]'