is there are any short cut method to find the determinant of A? Find the determinant  of A

$$A=\left(\begin{matrix} 
  x^1 & x^2 & x^3 \\
  x^8 & x^9 & x^4 \\
  x^7 & x^6 & x^5 \\
\end{matrix}\right)$$

My attempts : By  doing a laplace expansion along the first  column  i can calculate,but it is  a long process My question is that  is there  are  any short cut method  to find the determinant of A?
Thanks u

Use Gaussian elimination, while keeping track of changes to the determinant.
$$ \begin{aligned}
\left\lvert \begin{matrix} x^1 & x^2 & x^3 \\ x^8 & x^9 & x^4 \\ x^7 & x^6 & x^5 \end{matrix} \right\rvert
&= x^6 \left\lvert \begin{matrix} 1 & 1 & 1 \\ x^7 & x^7 & x^1 \\ x^6 & x^4 & x^2 \end{matrix} \right\rvert \\
&= x^6\left\lvert \begin{matrix} 1 & 0 & 0 \\ x^7 & 0 & x^1 - x^7 \\ x^6 & x^4 - x^6 & x^2 - x^6 \end{matrix} \right\rvert \\
&= x^6\left\lvert \begin{matrix}0 & x^1 - x^7 \\ x^4 - x^6 & x^2 - x^6 \end{matrix} \right\rvert \\
&= -x^{11}(1 - x^6)(1 - x^2)
\end{aligned}$$
