I'm unsure how I would factorise the following determinant
$$D =\begin{bmatrix} 1 & 1& 1\\ \lambda& \mu& \upsilon\\ \lambda^2 & \mu^2 & \upsilon^2 \end{bmatrix}$$
I have found the determinant. However, I don't really know where to go from there. I do however feel that I am missing something here regarding the properties of determinants but I am unsure what that would be. Any hints would be appreciated.
Hints : By column reduced operation, we have, $$D =\begin{bmatrix} 1 & 0& 0\\ \lambda& \mu-\lambda& \upsilon-\lambda\\ \lambda^2 & \mu^2-\lambda^2& \upsilon^2-\lambda^2 \end{bmatrix}$$
Given matrix and this matrix have their dets equal.
(As the rule , if $A$ is a square matrix. Let $B$ be the square matrix obtained from $A$ by adding a row to another row, or by adding a column to another column. Then $det(A)=det(B) $)