By using properties of determinants, prove the following: `|x+4 2x2x2xx+4 2x2x2xx+4|=(5x+4)(4-x)^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)

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

Using properties of determinants, solve the following for x: |[x-2, 2x-3, 3x-4],[x-4, 2x-9, 3x-16],[ x-8, 2x-27, 3x-64]|=0

By using properties of determinants.Show that: det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

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

Find each of the following products : (x^(3) - 2x^(2) + 5) xx (4x - 1)

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

Simplify each of the following x(x + 4) + 3x (2x^(2) - 1) + 4x^(2) + 4