Without expanding, show that the value of each of the determinants is zero: `|[(2x^2+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|`

Without expanding, show that the value of each of the determinants is zero: |[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|

Without expanding,show that the value of each of the determinants is zero: |(2x^(2)+2^(-x))^(2)quad (2^(x)-2^(-1))^(2),1(3^(x)+3^(-1))^(2),(3^(x)-3^(-x))^(2),1(4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1]|

|[2^(x)-2^(-x))^(2),(2^(x)+2^(-x))^(2),1(3^(x)-3^(-x))^(2),(3^(x)+3^(-x))^(2),1(4^(x)-4^(-x))^(2),(4^(x)+4^(-x))^(2),1]

If x,y,z in R , then the value of determinant |{:((2^x+2^(-x))^2,(2^x-2^(-x))^2,1),((3^x+3^(-x))^2,(3^x-3^(-x))^2,1),((4^x+4^(-x))^2,(4^x-4^(-x))^2,1):}| is equal to "............"

If x,y,zepsilonR then the value of |((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x))^(2),1),((3x^(x)+3^(-x))^(2),(3^(x)-3^(-x))^(2),1),((4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1)| is

If x,y,zepsilonR then the value of |((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x))^(2),1),((3x^(x)+3^(-x))^(2),(3^(x)-3^(-x))^(2),1),((4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1)| is

Without expanding, show that the value of each of the following determinants is zero: |1^2 2^2 3^2 4^2\ \ \ 2^2 3^2 4^2 5^2\ \ \ 3^2 4^2 5^2 6^2\ \ \ 4^2 5^2 6^2 7^2| (ii) |a b c a+2x b+2y c+2z x y z| (iii) |(2^x+2^(-x))^2(2^x-2^(-x))^2 1(3^x+3^(-x))^2(3^x-3^(-x))^2 1(4^x+4^(-x))^2(4^x-4^(-x))^2 1|

Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x^2)| has a factor (X-a)

Without expanding, find the value of: (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

The value of the determinant |{:(1+x,2,3,4),(1,2+x,3,4),(1,2,3+x,4),(1,2,3,4+x):}| is