`|[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2`

|[x+4,2x,2x] , [2x,x+4,2x] , [2x,2x,x+4]|=(5x+4)(x-4)^2

By using properties of determinants,prove the following ,2xdet[[x+4,2x,2x2x,x+4,2x2x,2x,x+4]]=(5x+4)(4-x)^(2)

If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

det [[x + 4,2x, 2x2x, x + 4,2x2x, 2x, x + 4]]

If |[2,4],[5,1]|=|[2x,4],[6,x]| then x is

(3x+4)(2x-3)+(5x-4)(x+2)

If f(x)=|{:(5+sin^2x,cos^2x,4sin2x),(sin^2x,5+cos^2x,4sin2x),(sin^2x,cos^2x,5+4sin2x):}| then evaluate

2x^2(x^3-x)-3x(x^4+2x)-2(x^2-3x^4)