FactorSteps - Maple Help

Student[Basics]

 FactorSteps
 generate steps in factoring polynomials

 Calling Sequence FactorSteps( expr, variable ) FactorSteps( expr, implicitmultiply = true )

Parameters

 expr - string or expression variable - (optional) variable to collect the terms by implicitmultiply - (optional) truefalse output = ... - (optional) option to control the return value displaystyle = ... - (optional) option to control the layout of the steps

Description

 • The FactorSteps command accepts a polynomial and displays the steps required to factor 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.
 • The output and displaystyle options are described in Student:-Basics:-OutputStepsRecord. The return value is controlled by the output option.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{FactorSteps}\left({x}^{3}+6{x}^{2}+12x+8\right)$
 $\begin{array}{lll}{}& {}& {{x}}^{{3}}{+}{6}{\cdot }{{x}}^{{2}}{+}{12}{\cdot }{x}{+}{8}\\ \text{▫}& {}& \text{1. Factor using Trial Evaluations}\\ {}& \text{◦}& \text{Rewrite in standard form}\\ {}& {}& {{x}}^{{3}}{+}{6}{}{{x}}^{{2}}{+}{12}{}{x}{+}{8}\\ {}& \text{◦}& \text{The factors of the constant coefficient}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}8\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{are:}\\ {}& {}& {C}{=}\left\{{1}{,}{2}{,}{4}{,}{8}\right\}\\ {}& \text{◦}& \text{Trial evaluations of}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{in}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{±}C\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{find}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{=}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}-2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{satisfies the equation, so}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x+2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{is a factor}\\ {}& {}& \genfrac{}{}{0}{}{\left({{x}}^{{3}}{+}{6}{}{{x}}^{{2}}{+}{12}{}{x}{+}{8}\right)}{\phantom{{x}{=}{-2}}}{|}\genfrac{}{}{0}{}{\phantom{\left({{x}}^{{3}}{+}{6}{}{{x}}^{{2}}{+}{12}{}{x}{+}{8}\right)}}{{x}{=}{-2}}{=}{0}\\ {}& \text{◦}& \text{Divide by}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x+2\\ {}& {}& \begin{array}{cc}\stackrel{\phantom{{{z}}^{{2}}}}{{x}{+}{2}}& \begin{array}{ccccc}{}& \phantom{{\mathrm{PP}}}{{x}}^{{2}}& \phantom{{P}}{+}{4}{}{x}& \phantom{{\mathrm{PP}}}{+}{4}& {}\\ {)}\phantom{{{x}}^{{2}}}& \phantom{{1}}{{x}}^{{3}}& \phantom{{1}}{+}{6}{}{{x}}^{{2}}& \phantom{{1}}{+}{12}{}{x}& \phantom{{1}}{+}{8}\\ {}& \multicolumn{2}{c}{\frac{{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}}{\phantom{{.}}}}& {}\\ {}& {}& \multicolumn{2}{c}{{4}{}{{x}}^{{2}}{+}{12}{}{x}}& {}& {}\\ {}& {}& \multicolumn{2}{c}{\frac{{4}{}{{x}}^{{2}}{+}{8}{}{x}}{\phantom{{.}}}}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{{4}{}{x}{+}{8}}& {}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{\frac{{4}{}{x}{+}{8}}{\phantom{{.}}}}& {}& {}& {}\\ {}& {}& {}& {}& {0}\hfill & {}& {}& {}& {}\end{array}\end{array}\\ {}& \text{◦}& \text{Quotient times divisor from long division}\\ {}& {}& \left({{x}}^{{2}}{+}{4}{}{x}{+}{4}\right){\cdot }\left({x}{+}{2}\right)\\ \text{•}& {}& \text{2. Examine term:}\\ {}& {}& {{x}}^{{2}}{+}{4}{}{x}{+}{4}\\ \text{▫}& {}& \text{3. Factor using the AC Method}\\ {}& \text{◦}& \text{Examine quadratic}\\ {}& {}& \left({\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}{}\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}{{4}}\right)\\ {}& \text{◦}& \text{Look at the coefficients,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}A{}{x}^{2}+B{}x+C\\ {}& {}& \left[{"A"}{=}{1}{,}{"B"}{=}{4}{,}{"C"}{=}{4}\right]\\ {}& \text{◦}& \text{Find factors of |AC| = |}1\cdot 4\text{| =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}4\\ {}& {}& \left\{{1}{,}{2}{,}{4}\right\}\\ {}& \text{◦}& \text{Find pairs of the above factors, which, when multiplied equal}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}4\\ {}& {}& \left\{{1}{\cdot }{4}{,}{2}{\cdot }{2}\right\}\\ {}& \text{◦}& \text{Which pairs of ± these factors have a}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{sum}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{of B =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}4\text{? Found:}\\ {}& {}& {2}{+}{2}{=}{4}\\ {}& \text{◦}& \text{Split the middle term to use above pair}\\ {}& {}& {{x}}^{{2}}{+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\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}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right){+}{4}\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the first group}\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\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}{{2}}\right)\right){+}\left({2}{}{x}{+}{4}\right)\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the second group}\\ {}& {}& {x}{\cdot }\left({x}{+}{2}\right){+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\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}{{2}}\right)\right)\\ {}& \text{◦}& x+2\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{is a common factor}\\ {}& {}& {x}{\cdot }\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}{{2}}\right){+}{2}{\cdot }\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}{{2}}\right)\\ {}& \text{◦}& \text{Group common factor}\\ {}& {}& \left({x}{+}{2}\right){\cdot }\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}{{2}}\right)\\ {}& {}& \text{This gives:}\\ {}& {}& {\left({x}{+}{2}\right)}^{{2}}\\ \text{•}& {}& \text{4. This gives:}\\ {}& {}& {\left({x}{+}{2}\right)}^{{3}}\end{array}$ (1)
 > $\mathrm{FactorSteps}\left({a}^{2}-{b}^{2}\right)$
 $\begin{array}{lll}{}& {}& {{a}}^{{2}}{-}{1}{\cdot }{{b}}^{{2}}\\ \text{•}& {}& \text{1. This is a difference of squares, in the form}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{A}^{2}-{B}^{2}\\ {}& {}& {{a}}^{{2}}{-}{{b}}^{{2}}\\ \text{•}& {}& \text{2. Apply difference of squares rule:}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{A}^{2}-{B}^{2}=\left(A+B\right){}\left(A-B\right)\\ {}& {}& \left({a}{+}{b}\right){}\left({a}{-}{b}\right)\end{array}$ (2)
 > $\mathrm{FactorSteps}\left({x}^{2}-x-12\right)$
 $\begin{array}{lll}{}& {}& {{x}}^{{2}}{-}{1}{\cdot }{x}{-}{12}\\ \text{▫}& {}& \text{1. Factor using the AC Method}\\ {}& \text{◦}& \text{Rewrite in standard form}\\ {}& {}& {{x}}^{{2}}{-}{x}{-}{12}\\ {}& \text{◦}& \text{Look at the coefficients,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}A{}{x}^{2}+B{}x+C\\ {}& {}& \left[{"A"}{=}{1}{,}{"B"}{=}{-1}{,}{"C"}{=}{-12}\right]\\ {}& \text{◦}& \text{Find factors of |AC| = |}1\cdot \left(-12\right)\text{| =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}12\\ {}& {}& \left\{{1}{,}{2}{,}{3}{,}{4}{,}{6}{,}{12}\right\}\\ {}& \text{◦}& \text{Find pairs of the above factors, which, when multiplied equal}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}12\\ {}& {}& \left\{{1}{\cdot }{12}{,}{2}{\cdot }{6}{,}{3}{\cdot }{4}\right\}\\ {}& \text{◦}& \text{Which pairs of ± these factors have a}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{difference}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{of B =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}-1\text{? Found:}\\ {}& {}& {3}{-}{4}{=}{-1}\\ {}& \text{◦}& \text{Split the middle term to use above pair}\\ {}& {}& {{x}}^{{2}}{+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}{}\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}{{4}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\right){-}{12}\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}x\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the first group}\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{x}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\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}{{3}}\right)\right){+}\left({-}{4}{}{x}{-}{12}\right)\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}-4\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the second group}\\ {}& {}& {x}{\cdot }\left({x}{+}{3}\right){+}\left(\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{-4}}\right)\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\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}{{3}}\right)\right)\\ {}& \text{◦}& x+3\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{is a common factor}\\ {}& {}& {x}{\cdot }\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}{{3}}\right){-}{4}{\cdot }\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}{{3}}\right)\\ {}& \text{◦}& \text{Group common factor}\\ {}& {}& \left({x}{-}{4}\right){\cdot }\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}{{3}}\right)\\ {}& {}& \text{This gives:}\\ {}& {}& \left({x}{-}{4}\right){\cdot }\left({x}{+}{3}\right)\end{array}$ (3)
 > $\mathrm{FactorSteps}\left(\frac{2{y}^{2}}{5}+\frac{113y}{5}+33\right)$
 $\begin{array}{lll}{}& {}& \frac{{2}}{{5}}{\cdot }{{y}}^{{2}}{+}\frac{{113}}{{5}}{\cdot }{y}{+}{33}\\ \text{•}& {}& \text{1. Remove rationals and common factor}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{5}}}{\cdot }\left({2}{}{{y}}^{{2}}{+}{113}{}{y}{+}{165}\right)\\ \text{•}& {}& \text{2. Examine term:}\\ {}& {}& {2}{}{{y}}^{{2}}{+}{113}{}{y}{+}{165}\\ \text{▫}& {}& \text{3. Factor using the AC Method}\\ {}& \text{◦}& \text{Examine quadratic}\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}}^{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{113}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{165}}\right)\\ {}& \text{◦}& \text{Look at the coefficients,}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}A{}{y}^{2}+B{}y+C\\ {}& {}& \left[{"A"}{=}{2}{,}{"B"}{=}{113}{,}{"C"}{=}{165}\right]\\ {}& \text{◦}& \text{Find factors of |AC| = |}2\cdot 165\text{| =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}330\\ {}& {}& \left\{{1}{,}{2}{,}{3}{,}{5}{,}{6}{,}{10}{,}{11}{,}{15}{,}{22}{,}{30}{,}{33}{,}{55}{,}{66}{,}{110}{,}{165}{,}{330}\right\}\\ {}& \text{◦}& \text{Find pairs of the above factors, which, when multiplied equal}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}330\\ {}& {}& \left\{{1}{\cdot }{330}{,}{2}{\cdot }{165}{,}{3}{\cdot }{110}{,}{5}{\cdot }{66}{,}{6}{\cdot }{55}{,}{10}{\cdot }{33}{,}{11}{\cdot }{30}{,}{15}{\cdot }{22}\right\}\\ {}& \text{◦}& \text{Which pairs of ± these factors have a}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{sum}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{of B =}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}113\text{? Found:}\\ {}& {}& {3}{+}{110}{=}{113}\\ {}& \text{◦}& \text{Split the middle term to use above pair}\\ {}& {}& {2}{}{{y}}^{{2}}{+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{110}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\right){+}{165}\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}y\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the first group}\\ {}& {}& \left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\right)\right){+}\left({110}{}{y}{+}{165}\right)\\ {}& \text{◦}& \text{Factor}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}55\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{out of the second group}\\ {}& {}& {y}{\cdot }\left({2}{}{y}{+}{3}\right){+}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{55}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\right)\right)\\ {}& \text{◦}& 2{}y+3\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}\text{is a common factor}\\ {}& {}& {y}{\cdot }\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\right){+}{55}{\cdot }\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\right)\\ {}& \text{◦}& \text{Group common factor}\\ {}& {}& \left({y}{+}{55}\right){\cdot }\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}{}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{y}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\right)\\ {}& {}& \text{This gives:}\\ {}& {}& \left({y}{+}{55}\right){\cdot }\left({2}{}{y}{+}{3}\right)\\ \text{•}& {}& \text{4. This gives:}\\ {}& {}& \frac{{1}}{{5}}{\cdot }\left({y}{+}{55}\right){\cdot }\left({2}{}{y}{+}{3}\right)\end{array}$ (4)

Compatibility

 • The Student[Basics][FactorSteps] command was introduced in Maple 2021.