Using properties of determinants, show that `|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, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

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

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

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

3. Using properties of determinants, show that :|[b+c,a,b] , [c+a,c,a] , [a+b,b,c]| = (a + b + c) (a-c)^2

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

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

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