If the determinant x+a    p+u   l+fy+b  q+v    m+gz+c   r+w   n+hsplits into exactly k determinants of order 3, each element of which contains only one term, then the value of k is

since,x+a    p+u   l+fy+b  q+v    m+gz+c   r+w   n+h=   x        p          ly+b  q+v    m+gz+c   r+w   n+h +  a        u           fy+b  q+v    m+gz+c   r+w   n+hsplitting first row=   x        p          l   y       q         mz+c   r+w   n+h +   x        p          l   b       v         gz+c   r+w   n+h+  a        u           f  y         q        mz+c   r+w   n+h+  a        u           f  b         v          gz+c   r+w   n+h                                                                                                                                                splitting second rowSimilarly we can split these 4 determinants in 8 determinants by splitting each one in two determinants further. So, k=8