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Using the properties of determinants, prove that
Using the properties of determinants, prove that
$\begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{vmatrix} = (a - b)(b - c)(c - a)(a + b + c)$
Given: $\begin{vmatrix} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{vmatrix}$
To show: (a - b)(b - c)(c - a)(a + b + c)
Answer
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From ISC 2025 Improvement Mathematics Paper 1, question 7.