Prove that `|[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3`

Prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(a-1)^(3)

Using properties of determinants,prove that det[[a^(2)+2a,2a+1,12a+1,a+2,13,3,1]]=(a-1)^(3)

Show that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

Prove that, |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

Using properties of determinants, prove that |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|=-2

D=|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}| then,

Using properties of determinants, prove the following: |[1,a,a^2],[a^2,1,a],[a,a^2,1]|=(1-a^3)^2