Factorizing Determinants I don't know how to factorize the determinants. Please help.
1.
$$
\begin{vmatrix}
a+b &b+c &c+a\\
b+c &c+a &a+b\\
c+a &a+b &b+c
\end{vmatrix}
$$
2.
$$
\begin{vmatrix}
a^2 &b^2 &c^2\\
b^2 &c^2 &a^2\\
c^2 &a^2 &b^2
\end{vmatrix}
$$

Using Saruss' rule you should easily see that the determinant of a matrix of the form
$$\left(\begin{matrix}x&y&z\\y&z&x\\z&x&y\end{matrix}\right)$$
is $3xyz-x^3-y^3-z^3$.
Can you use this to solve your problems?
