Exercise & Solution Page

The macros $ and $ don't survive \xdef. Use $:

\newcommand{\STA}
{%
 \InitVariablesSTA
 \newcommand{\factored}{$(x+\bvar)(x+\dvar)$}%
 \newcommand{\expanded}{\(x^2+{\Bvar}x+\Cvar\)}%
}

enter image description here

Related: Build tabular content via \foreach

You might use \protected@xdef, so $ and $ might be used; it's simpler the other way.

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