** Using WeBWorK **

Here are some comments about our code:

    loadMacros(
      "PGstandard.pl",
      "Parser.pl",
      "MathObjects.pl",
      "contextLimitedPolynomial.pl"
    );

You don't need both Parser.pl and MathObjects.pl here. Use MathObjects.pl by itself, as Parser.pl is depricated.

    TEXT(&beginproblem);

The ampersand is not needed here (it is not an error, but is a left-over from older versions of Perl when it was needed).

    ######################################
    #  Setup

    Context("Numeric");

    #Note: I have to change the context to Numeric or I get an error when I define $a below. 
    #Note: I thought Numeric was the default and that to change 
    #          context, one needed to explicitly declare a new
    #          context not just load the context_____.pl file.

You are right, that is how it SHOULD work, but a number of the context files DO set the context. That needs to change, but I haven't done it yet. It is left over from earlier program styles and changing it will require some problems to be modified. That makes it harder to change the macro files.

    Context()->variables->add(y=>'Real');

You may want to use variables->are() rather than variables->add(). The former will mean that the only variable is y rather than both x and y.

    $a1 = random(2,6,1);
    $a2 = random(3,5,1);
    $a3 = non_zero_random(-9,9,1);
    $a4 = random(2,9,1);
    $a5 = random(1,5,1);
    $a = Formula ("$a1 ($a2 y + $a3) - ($a4 y + $a5)")->reduce;

    $b1 = random(2,4,1);
    $b2 = random(2,4,1);
    $b3 = random(2,8,1);
    $b4 = random(2,7,1);
    $b5 = random(1,4,1);
    $b = Formula("$b1-$b2 [ $b3 -($b4 y - $b5)]");

    #Note: $b is not working. The TeX is replacing the brackets with parenthesis.

You are right, the TeX method does not alternate parenthesis types, as the string method does. (The actual parentheses you type in are not retained within the formula.) It would require altering the MathObject code to change this behavior.

    ######################################
    #  Main text

    BEGIN_TEXT
    Simplify each algebraic expression:
    $BR Note:  In this problem, the variable is \(y\).
    $PAR
    a) \( \{$a->TeX\} = \) \{ ans_rule(10) \} 
    $PAR
    b) \( $b1-$b2 [$b3 -($b4 y - $b5)] = \) \{ ans_rule(10) \} 
    $BR

    END_TEXT

Note that the final $BR is not needed.

    ######################################
    #  Answers

    Context("LimitedPolynomial")->flags->set(singlePowers=>1);
    Context()->variables->add(y=>'Real');

    #Note:  I have already declared y to be a variable above
    #         but I get an error message that it is not defined
    #         unless I declare it again before I use y below.

Each context has its own set of variables. You added y to the Numeric context above, but that does not affect this new context. So you really DO have to add it again.

    $ans_a = "($a1*$a2-$a4) y + ($a1*$a3-$a5)";
    ANS(Formula($ans_a)->reduce->cmp);

    #Note: If I use
    #$ans_a = Formula("($a1*$a2-$a4) y + ($a1*$a3-$a5)")->reduce;
    #ANS($ans_a->cmp);
    #    I get an error about the multiplcation in the coeffiecients.

    $ans_b = "($b2*$b4) y +($b1 - ($b2*$b3) - ($b2*$b5))";
    ANS(Formula($ans_b)->reduce->cmp);

I am not able to reproduce the error you have been seeing. I also don't see how the two forms would be able to produce different results, as they should be identical (whether you use a string literal or a variable holding the string should not make any difference). Are you sure you didn't change anything else?

Davide