Without expanding show that : `|(23,12,11),(36,10,26),(63,26,37)|=0`

Without expanding show that : |(a,b+c,1),(b,c+a,1),(c,a+b,1)|=0

Without expanding show that : |(bc,a,a^2),(ca,b,b^2),(ab,c,c^2)|=|(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3)|

Without expanding show that : |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=|(1,bc,b+c),(1,ca,c+a),(1,ab,a+b)|

Without expanding show that : |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)|=0

Without expanding show that : |(1,bc,bc(b+c)),(1,ca,ca(c+a)),(1,ab,ab(a+b))|=0

Without expanding show that : |(x-y,y-z,z-x),(y-z,z-x,x-y),(z-x,x-y,y-z)|=0

Without expanding show 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)|

Without expanding show that : |(""^xC_r,""^xC_(r+1),""^xC_(r+2)),(""^yC_r,""^yC_(r+1),""^yC_(r+2)),(""^zC_r,""^zC_(r+1),""^zC_(r+2))|=|(""^xC_r,""^(x+1)C_(r+1),""^(x+2)C_(r+2)),(""^yC_r,""^(y+1)C_(r+1),""^(y+2)C_(r+2)),(""^zC_r,""^(z+1)C_(r+1),""^(z+2)C_(r+2))|

Find the value of : |(1,1^2,1^3),(1,2^2,2^3),(1,3^2,3^3)|

Without expanding at any stage, find the value of |(0,a,-b),(-a,0,c),(b,-c,0)| .