The ExpandSteps command accepts a product of polynomials and displays the steps required to expand the expression.

If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.  

The implicitmultiply option is only relevant when expr is a string.  This option is passed directly on to the InertForm:-Parse command and will cause things like 2x to be interpreted as 2*x, but also, xyz to be interpreted as x*y*z.

A step may show up where the expression is not obviously different from the previous step.  This can happen when the underlying data structure is transformed during the step, and it is not obvious that the resulting structure is the same as the original, but just expressed differently.  This becomes more apparent when looking at the inert form of the raw data.

The return value is a module that displays annotated steps by default.  This module also has callable methods and data members: data, numsteps, step, and toMathML.  

This function is part of the Student:-Basics package.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right)\:$

$\mathrm{ExpandSteps}\left(\frac{a^2-1}{\frac{a}{3}+\frac{1}{3}}\right)$

$\begin{array}{c}\frac{a^2-1}{\frac{a}{3}+\frac{1}{3}}\\ \=\frac{\left(a+1\right)\cdot \left(a-1\right)}{\left(a+1\right)\cdot \left(\frac{1}{3}\right)}& \left(\text{Factor}\right)\\ \=\frac{a-1}{\frac{1}{3}}& \left(\text{divide}\right)\\ \=\left(a-1\right)\cdot \left(\frac{3}{1}\right)& \left(\text{Rewrite division as multiplication by reciprocal}\right)\\ \=3a-3& \left(\text{Multiply fraction and reduce by gcd}\right)\end{array}$

$\mathrm{ex}≔\mathrm{ExpandSteps}\left(3a\left(4a-y+42\right)\right)$

$\mathrm{ex}≔\begin{array}{c}3\cdot a\cdot \left(4\cdot a-1\cdot y+42\right)\\ \=12a^2-3ay+126a& \left(\text{Multiply through:}3a\cdot \left(4a-y+42\right)\text{=}12a^2-3ay+126a\right)\end{array}$

$\mathrm{ex}:-\mathrm{numsteps}$

$2$

$\mathrm{ex}:-\mathrm{step}\left(2\right)$

$\begin{array}{cc}12a^2-3ay+126a& \left(\text{Multiply through:}3a\cdot \left(4a-y+42\right)\text{=}12a^2-3ay+126a\right)\end{array}$

$\mathrm{ex}:-\mathrm{toMathML}\left(\right)$

$\mathrm{ExpandSteps}\left(''(1+1)*(3-1)''\right)$

$\begin{array}{c}\left(1+1\right)\cdot \left(3-1\right)\\ \=2\cdot \left(3-1\right)& \left(\text{Add terms}\right)\\ \=2\cdot 2& \left(\text{Add terms}\right)\\ \=4& \left(\text{Multiply constants}\right)\end{array}$

$\mathrm{ExpandSteps}\left(''2.1yx^2/(4.3xy)''\,'\mathrm{implicitmultiply}'\right)$

$\begin{array}{c}\frac{2.1\cdot y\cdot x^2}{4.3\cdot x\cdot y}\\ \=\frac{2.1\cdot x^2}{4.3\cdot x}& \left(\text{divide out common terms}\right)\\ \=\frac{2.100000000x}{4.3}& \left(\text{divide out common terms}\right)\\ \=0.4883720930x& \left(\text{Divide constants}\right)\end{array}$

The Student[Basics][ExpandSteps] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.