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If then show that , using properties of determinant.
If $x + y + z = 0$ then show that $\begin{vmatrix} 1 & 1 & 1 \\ x & y & z \\ x^3 & y^3 & z^3 \end{vmatrix} = 0$, using properties of determinant.
Given: x + y + z = 0
To show: \begin{vmatrix} 1 & 1 & 1 \\ x & y & z \\ x^3 & y^3 & z^3 \end{vmatrix} = 0
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From ISC 2025 Mathematics Paper 1, question 7.