By using properties of determinants. Show that:
(i) `|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a)`
(ii) `|[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)`

Explanation

To solve the given determinants using properties of determinants, we will break down the solution into two parts as specified in the question.

### Part (i)
We need to show that:
\[ | \begin{bmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{bmatrix} | = (a-b)(b-c)(c-a) \]

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