SimplifySteps - Maple Help

Student[Basics]

 SimplifySteps
 show steps in the simplification of a specified expression

 Calling Sequence SimplifySteps(ex, opts)

Parameters

 ex - expression or string opts - options of the form keyword=value where keyword is one of displaystyle, output

Description

 • The SimplifySteps command is used to show the steps of simplifying a basic student 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 fullsolution option can be used to show additional arithmetic steps in the simplification.
 • The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{SimplifySteps}\left("2*75^\left(1/2\right)-5*27^\left(1/2\right)"\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& {2}{\cdot }{{75}}^{\frac{{1}}{{2}}}{-}{5}{\cdot }{{27}}^{\frac{{1}}{{2}}}\\ \text{•}& {}& \text{Factor roots}\\ {}& {}& {2}{\cdot }\left({5}{\cdot }\sqrt{{3}}\right){-}{1}{\cdot }\left({5}{\cdot }\left({3}{\cdot }\sqrt{{3}}\right)\right)\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\cdot \left(5{}\sqrt{3}\right)\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{10}}{}\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}\right){-}{1}{\cdot }\left({5}{\cdot }\left({3}{\cdot }{{3}}^{\frac{{1}}{{2}}}\right)\right)\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}5\cdot \left(3{}\sqrt{3}\right)\\ {}& {}& {10}{}\sqrt{{3}}{-}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{15}}{}\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}\right)\\ \text{•}& {}& \text{Add}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}10{}\sqrt{3}-15{}\sqrt{3}\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{-}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{5}}{}\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}\right)\end{array}$ (1)
 > $\mathrm{SimplifySteps}\left("\left(5\right)^\left(1/2\right)/\left(2*\left(10\right)^\left(1/2\right)*\left(2\right)^\left(1/2\right)\right)"\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \frac{{{5}}^{\frac{{1}}{{2}}}}{{2}{\cdot }{{10}}^{\frac{{1}}{{2}}}{\cdot }{{2}}^{\frac{{1}}{{2}}}}\\ \text{•}& {}& \text{Multiply in order to rationalize the denominator}\\ {}& {}& \frac{\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{10}}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}}{\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{10}}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\sqrt{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}}{\cdot }\left(\frac{\sqrt{{5}}}{{2}{}\sqrt{{10}}{}\sqrt{{2}}}\right)\\ \text{•}& {}& \text{Multiply the denominator}\\ {}& {}& \frac{\sqrt{{10}}{\cdot }\sqrt{{2}}{\cdot }\sqrt{{5}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{40}}}\\ \text{•}& {}& \text{Factor roots}\\ {}& {}& \frac{\sqrt{{2}}{\cdot }\sqrt{{5}}{\cdot }\sqrt{{2}}{\cdot }\sqrt{{5}}}{{40}}\\ \text{•}& {}& \text{Combine}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\left\{\sqrt{2}\cdot \sqrt{2},\sqrt{5}\cdot \sqrt{5}\right\}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{\cdot }\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{5}}}{{40}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\cdot 5\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{10}}}{{40}}\\ \text{•}& {}& \text{Cancel out factor of}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}10\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}}\end{array}$ (2)
 > $\mathrm{SimplifySteps}\left("\left(k^4\right)^\left(5*a\right)/\left(k^3*k^6\right)",\mathrm{output}=\mathrm{typeset}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& \frac{{\left({{k}}^{{4}}\right)}^{{5}{\cdot }{a}}}{{{k}}^{{3}}{\cdot }{{k}}^{{6}}}\\ \text{•}& {}& \text{Apply the integer power of a power rule,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\left({a}^{n}\right)}^{m}={a}^{n{}m}\\ {}& {}& \frac{{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{k}}}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{5}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\right)}}{{{k}}^{{3}}{\cdot }{{k}}^{{6}}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}4\cdot \left(5{}a\right)\\ {}& {}& \frac{{{k}}^{\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{20}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\right)}}{{{k}}^{{3}}{\cdot }{{k}}^{{6}}}\\ \text{•}& {}& \text{Apply the product rule}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{a}^{n}{}{a}^{m}={a}^{n+m}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{to add exponents with common base}\\ {}& {}& \frac{{{k}}^{{20}{}{a}}}{{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{k}}}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}}}\\ \text{•}& {}& \text{Add exponents}\\ {}& {}& \frac{{{k}}^{{20}{}{a}}}{{{k}}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{9}}}}\\ \text{•}& {}& \text{Divide}\\ {}& {}& {{k}}^{{-}{9}{+}{20}{}{a}}\end{array}$ (3)
 > $\mathrm{SimplifySteps}\left(\mathrm{sin}\left(x+{\mathrm{sin}\left(x\right)}^{2}+{\mathrm{cos}\left(x\right)}^{2}\right)\mathrm{csc}\left(x+1\right),\mathrm{mode}=\mathrm{Learn}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's simplify}\\ {}& {}& {\mathrm{sin}}{}\left({x}{+}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}\right){\cdot }{\mathrm{csc}}{}\left({x}{+}{1}\right)\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Reciprocal Function}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\mathrm{csc}{}\left(x+1\right)=\frac{1}{\mathrm{sin}{}\left(x+1\right)}\\ {}& {}& {\mathrm{sin}}{}\left({x}{+}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}\right){}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{sin}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\right)}\\ \text{•}& {}& \text{Apply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{Pythagoras}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{trig identity,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\mathrm{sin}{}\left(x\right)}^{2}=1-{\mathrm{cos}{}\left(x\right)}^{2}\\ {}& {}& \frac{{\mathrm{sin}}{}\left({x}{+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{-}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\mathrm{cos}}}{}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right)}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}\right){+}{{\mathrm{cos}}{}\left({x}\right)}^{{2}}\right)}{{\mathrm{sin}}{}\left({x}{+}{1}\right)}\\ \text{•}& {}& \text{Evaluate}\\ {}& {}& {1}\end{array}$ (4)

Compatibility

 • The Student[Basics][SimplifySteps] command was introduced in Maple 2022.