Solution Steps - Maple Help

 Solution Steps

Maple 2021 includes numerous new algorithms for showing step-by-step solutions for a variety of problems in mathematics.

Long Division

The LongDivision command gives a visual solution to an arithmetic or polynomial long division problem, showing all of the intermediate steps.

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{LongDivision}\left(48{x}^{4}+284{x}^{3}+620{x}^{2}+593x+210,2x+3\right)$
 $\begin{array}{cc}\stackrel{\phantom{\frac{{{x}}^{{2}}}{{2}}}}{{\mathrm{%+}}{}\left({2}{}{x}{,}{3}\right)}& \begin{array}{cccccc}{}& {24}{}{{x}}^{{3}}& {+}{106}{}{{x}}^{{2}}& {+}{151}{}{x}& {+}{70}& {}\\ {)}\phantom{{{x}}^{{2}}}& \phantom{{1}}{48}{}{{x}}^{{4}}& \phantom{{1}}{+}{284}{}{{x}}^{{3}}& \phantom{{1}}{+}{620}{}{{x}}^{{2}}& \phantom{{1}}{+}{593}{}{x}& \phantom{{1}}{+}{210}\\ {}& \multicolumn{2}{c}{\frac{{48}{}{{x}}^{{4}}{+}{72}{}{{x}}^{{3}}}{\phantom{{.}}}}& {}\\ {}& {}& \multicolumn{2}{c}{{212}{}{{x}}^{{3}}{+}{620}{}{{x}}^{{2}}}& {}& {}\\ {}& {}& \multicolumn{2}{c}{\frac{{212}{}{{x}}^{{3}}{+}{318}{}{{x}}^{{2}}}{\phantom{{.}}}}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{{302}{}{{x}}^{{2}}{+}{593}{}{x}}& {}& {}& {}\\ {}& {}& {}& \multicolumn{2}{c}{\frac{{302}{}{{x}}^{{2}}{+}{453}{}{x}}{\phantom{{.}}}}& {}& {}& {}\\ {}& {}& {}& {}& \multicolumn{2}{c}{{140}{}{x}{+}{210}}& {}& {}& {}& {}\\ {}& {}& {}& {}& \multicolumn{2}{c}{\frac{{140}{}{x}{+}{210}}{\phantom{{.}}}}& {}& {}& {}& {}\\ {}& {}& {}& {}& {}& {0}\hfill & {}& {}& {}& {}& {}\end{array}\end{array}$ (1.1)
 >
 (1.2)

Factoring

The FactorSteps command shows the steps in factoring a polynomial.

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{FactorSteps}\left({x}^{3}+6{x}^{2}+12x+8\right)$
 $\begin{array}{lll}{}& {}& \left[{}\right]\\ \text{â–«}& {}& \text{1. Trial Evaluations}\\ {}& \text{â—¦}& \text{Rewrite in standard form}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& \text{The factors of the constant coefficient}8\text{are:}\\ {}& {}& {C}{=}\left\{{1}{,}{2}{,}{4}{,}{8}\right\}\\ {}& \text{â—¦}& \text{Trial evaluations of}x\text{in}\text{Â±}C\text{find}x\text{=}-2\text{satisfies the equation, so}x+2\text{is a factor}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& \text{Divide by}x+2\\ {}& {}& \begin{array}{cc}\stackrel{\phantom{\frac{{{x}}^{{2}}}{{2}}}}{\left[{}\right]}& \begin{array}{ccccc}{}& {{x}}^{{2}}& {+}{4}{}{x}& {+}{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{â—¦}& \text{Quotient times divisor from long division}\\ {}& {}& \left[{}\right]\\ \text{â€¢}& {}& \text{2. Examine term:}\\ {}& {}& {{x}}^{{2}}{+}{4}{}{x}{+}{4}\\ \text{â–«}& {}& \text{3. Apply the AC Method}\\ {}& \text{â—¦}& \text{Examine quadratic}\\ {}& {}& \left(\left[\colorbox[rgb]{1,1,0.631372549019608}{{}}\right]\right)\\ {}& \text{â—¦}& \text{Look at the coefficients,}A{}{x}^{2}+B{}x+C\\ {}& {}& \left[{"A"}{=}{1}{,}{"B"}{=}{4}{,}{"C"}{=}{4}\right]\\ {}& \text{â—¦}& \text{Find factors of |AC| = |}1\cdot 4\text{| =}4\\ {}& {}& \left\{{1}{,}{2}{,}{4}\right\}\\ {}& \text{â—¦}& \text{Find pairs of the above factors, which, when multiplied equal}4\\ {}& {}& \left\{\left[{}\right]{,}\left[{}\right]\right\}\\ {}& \text{â—¦}& \text{Which pairs of these factors have a}\text{sum}\text{of B =}4\text{? Found:}\\ {}& {}& \left[{}\right]{=}{4}\\ {}& \text{â—¦}& \text{Split the middle term to use above pair}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& \text{Factor}x\text{out of the first pair}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& \text{Factor}2\text{out of the second pair}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& x+2\text{is a common factor}\\ {}& {}& \left[{}\right]\\ {}& \text{â—¦}& \text{Group common factor}\\ {}& {}& \left[{}\right]\\ {}& {}& \text{This gives:}\\ {}& {}& \left[{}\right]\\ \text{â€¢}& {}& \text{4. This gives:}\\ {}& {}& \left[{}\right]\end{array}$ (2.1)



Solve

The SolveSteps command shows the steps in solving an equation or system of equations

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{SolveSteps}\left(5{ⅇ}^{4x}=16\right)$