Show without expanding at any stage that: ` | [1,bc, a(b+c)],[1,ca, b(c+a)],[1,ab, c(a+b)]|=0 `

Without expanding at any state, prove that |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|=0

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

Show without expanding at any stage that: [1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

Using the property of determinants and without expanding , prove that: |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 0

Show without expanding at any stage that: [0,a,-b],[-a,0,-c],[b,c,0]|=0

Show without expanding at any stage that: [1/a, a^2, bc],[1/b, b^2, ca],[1/c, c^2, ab]|=0

Show without expanding at stage that : det[[1,ca,b(c+a)1,ab,c(a+b)]]=0

Show without expanding at any stage that: [x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Show without expanding at any stage that: [1,a,bc],[1,b,ca],[1,c,ab]|=|[1,a,a^2],[1,b,b^2],[1,c,c^2 ]|

Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a) ),(1, ab , c( a+ b)):}|=0 .