Math Help - Determine the value of (1+xyz)

1. Determine the value of (1+xyz)

If $x,y,z$are all different and given that

$
\begin{vmatrix}
x & x^2 & 1+x^3 \\
y & y^2 & 1+y^3 \\
z & z^2 & 1+z^3
\end{vmatrix} = 0
$

Determine the value of $(1+xyz).$

2. Originally Posted by varunnayudu
If $x,y,z$are all different and given that

$
\begin{vmatrix}
x & x^2 & 1+x^3 \\
y & y^2 & 1+y^3 \\
z & z^2 & 1+z^3
\end{vmatrix} = 0
$

Determine the value of $(1+xyz).$
it will be good if you will give some of your initial computations.

3. Originally Posted by varunnayudu
If $x,y,z$are all different and given that

$
\begin{vmatrix}
x & x^2 & 1+x^3 \\
y & y^2 & 1+y^3 \\
z & z^2 & 1+z^3
\end{vmatrix} = 0
$

Determine the value of $(1+xyz).$
Do you know that if A and B are matrices such that they differ in one row or column, then det(A + B) = det(A) + det(B) ?

Also do you know that $\begin{vmatrix}
1 & x & x^2 \\
1 & y & y^2 \\
1 & z & z^2
\end{vmatrix} = (x-y)(y-z)(z-x)$
?