Without expanding show that, if s= a +b +c, then 2s is a factor of
` |{:( s+c, a,b),(c, s+a, b),(c,a,s+b):}|`

If s=(a+b+c),then value of |{:(s+c,a,b),(c,s+a,b),(c,a,s+b):}| is

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |[a, b, c], [b, c, a], [c, a, b]|

Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+b|=0 .

Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Without expanding the determinant, show that (a+b+c) is a factor of the determinant of . \begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{pmatrix}

Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2b^2,a b ,a+b]|=0

If c^2 = a^2 + b^2, 2s = a + b + c , then 4s(s-a) (s - b)(s-c)

Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b),( a-c ,b-c,0)|=0 .

Let a+b+c =s and |{:(s+c,,a,,b),(c,,s+a,,b),(c,,a,,s+b):}|=432 then the value of s is "____"

If c^(2) = a^(2) + b^(2) , then prove that 4s (s - a) (s - b) (s - c) = a^(2) b^(2)