Show that $\displaystyle \det \begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{bmatrix} = (b-a)(c-a)(c-b) $.

Using expansion by minors I got $\displaystyle c^{2}(b-a) + b^{2}(a-c) + a^{2}(c-b) $. How would I convert this to the above form?