Question: Why does `simplify` fail to rewrite certain sub-expressions?

kernelopts('version');

Physics:-Version();

with(RealDomain):

eval(MTM:-det(<
   a, b/2, d/2 |
   b/2, c, e/2 |
   d/2, e/2, f
  >), PDETools:-Solve(MTM:-det(<
     x**2 + y**2, x1**2 + y1**2, x2**2 + y2**2, x3**2 + y3**2 |
     x, x1, x2, x3 |
     y, y1, y2, y3 |
     1, 1, 1, 1
    >) = inner([a, b, c, d, e, f], [x**2, x*y, y**2, x, y, 1]),
   {f, e, d, c, b, a}, 'independentof' = {y, x}))/MTM:-det(<
  x1, x2, x3 |
  y1, y2, y3 |
  1, 1, 1
 >): simplify(`%`);

eval(MTM:-det(<
   a, b/2, d/2 |
   b/2, c, e/2 |
   d/2, e/2, f
  >), PDETools:-Solve(MTM:-det(<
     x**2 - y**2, x1**2 - y1**2, x2**2 - y2**2, x3**2 - y3**2, x4**2 - y4**2 |
     x*y, x1*y1, x2*y2, x3*y3, x4*y4 |
     x, x1, x2, x3, x4 |
     y, y1, y2, y3, y4 |
     1, 1, 1, 1, 1
    >) = inner([a, b, c, d, e, f], [x**2, x*y, y**2, x, y, 1]),
   {f, e, d, c, b, a}, 'independentof' = {y, x}))/(MTM:-det(<
   x2, x3, x4 | 
   y2, y3, y4 | 
   1, 1, 1
  >)*MTM:-det(<
   x3, x4, x1 | 
   y3, y4, y1 | 
   1, 1, 1
  >)*MTM:-det(<
   x4, x1, x2 | 
   y4, y1, y2 | 
   1, 1, 1
  >)*MTM:-det(<
   x1, x2, x3 | 
   y1, y2, y3 | 
   1, 1, 1
  >)): simplify(`%`);