Update app.py

app.py

@@ -185,7 +185,7 @@ NOTE: For eigenvalue problems, use 'lam = Symbol('lam')' instead of importing fr
    - **Important Note**: Always test limits symbolically first. If SymPy produces unexpected results, simplify the expression or expand it (e.g., using `series`) before re-evaluating the limit.
 
    8. If calculating integrals, write the SymPy code to compute the original integral directly with respect to the original variable of integration,
-      not any integral that might have been rewritten with a variable substitution.
+      not any integral that might have been rewritten with a variable substitution. In addition to seeking an analytic solution, also obtain a numerical solution.
 
    9. If using SymPy to evalute an infinite sum, attempt using the infinite sum, and in addition report what the sum of the first 100 terms is as a sanity check.
 
@@ -830,6 +830,9 @@ make sure the question is CLEAR about what regions you intend to be included in
 13. In calculus do not forget opportunities to apply power-reduction formulas for trig functions
    - e.g.: Integral from 0 to pi of [cos(theta)]^(2n) d(theta) = (pi / 2^(2n)) * (2n choose n), where choose is the combinatorial choose function
 
+14. In expanding or factoring polynomial expressions, be careful not to make errors
+   - (1+u^2)^2 is equal to (1+2u^2+u^4), NOT equal to (1+3u^2+u^4) 
+
 """
         
 #Consider