∣∣∣∣∣1aa21bb21cc2∣∣∣∣∣=(a−b)(b−c)(c−a) ∣�

1.	∣∣∣∣∣1aa21bb21cc2∣∣∣∣∣=(a−b)(b−c)(c−a) ∣∣∣∣111abca3b3c3∣∣∣∣=(a−b)(b−c)(c−a)(a+b+c)
Answer» $∣ ∣∣∣ ∣ \begin{matrix} 1 & a & a^{2} 1 & b & b^{2} 1 & c & c^{2} \end{matrix} ∣ ∣∣∣ ∣ = (a - b) (b - c) (c - a)$ $∣ ∣∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣∣ ∣ = (a - b) (b - c) (c - a) (a + b + c)$

∣∣∣∣∣1aa21bb21cc2∣∣∣∣∣=(a−b)(b−c)(c−a) ∣∣∣∣111abca3b3c3∣∣∣∣=(a−b)(b−c)(c−a)(a+b+c)

Answer»

$∣ ∣∣∣ ∣ \begin{matrix} 1 & a & a^{2} 1 & b & b^{2} 1 & c & c^{2} \end{matrix} ∣ ∣∣∣ ∣ = (a - b) (b - c) (c - a)$

$∣ ∣∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣∣ ∣ = (a - b) (b - c) (c - a) (a + b + c)$