Distributiviteit \((a+r)(b+s)\)

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  1. \((\frac{4}{18}+p)(p-\frac{-17}{14})\)
  2. \((\frac{14}{3}-b)(b-\frac{-3}{6})\)
  3. \((\frac{-10}{16}+b)(\frac{13}{18}-a)\)
  4. \((\frac{6}{20}+x)(q-\frac{1}{12})\)
  5. \((\frac{-13}{20}-a)(b+\frac{-19}{20})\)
  6. \((x+\frac{-18}{16})(\frac{4}{16}+q)\)
  7. \((\frac{7}{17}-b)(\frac{-16}{14}-a)\)
  8. \((a-\frac{11}{2})(b+\frac{16}{20})\)
  9. \((\frac{-13}{5}-b)(\frac{4}{19}+p)\)
  10. \((\frac{-5}{7}+p)(x-\frac{-15}{5})\)
  11. \((a-\frac{-5}{14})(\frac{14}{14}-p)\)
  12. \((x+\frac{5}{16})((-6)-p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{18}+p)(p-\frac{-17}{14})& =(\color{red}{p}+\color{orange}{\frac{2}{9}}).(\color{green}{p}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{14}p+\frac{2}{9}p+\frac{2}{9}.\frac{17}{14}& \text{Uitwerken } \\ & =p^2+(\frac{17}{14}+\frac{2}{9})p+\frac{34}{126} & \text{Neem samen} \\ &=p^2+\frac{181}{126}p+\frac{34}{126} & \text{Maak de som} \\ &=p^2+\frac{181}{126}p+\frac{17}{63} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{3}-b)(b-\frac{-3}{6})& =(\color{red}{-b}+\color{orange}{\frac{14}{3}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{2}b+\frac{14}{3}b+\frac{14}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{2})+\frac{14}{3})b+(\frac{-14}{6}) & \text{Neem samen} \\ &=-b^2+\frac{25}{6}b+(\frac{-14}{6}) & \text{Maak de som} \\ &=-b^2+\frac{25}{6}b+(\frac{-7}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{16}+b)(\frac{13}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{8}}).(\color{green}{-a}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{18}b+\frac{5}{8}a-\frac{5}{8}.\frac{13}{18}& \text{Uitwerken } \\ & =-ab+\frac{13}{18}b+\frac{5}{8}a-\frac{65}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{20}+x)(q-\frac{1}{12})& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{12}x+\frac{3}{10}q-\frac{3}{10}.\frac{1}{12}& \text{Uitwerken } \\ & =qx-\frac{1}{12}x+\frac{3}{10}q-\frac{3}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{12}x+\frac{3}{10}q-\frac{1}{40} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-13}{20}-a)(b+\frac{-19}{20})& =(\color{red}{-a}+\color{orange}{\frac{-13}{20}}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{20}a-\frac{13}{20}b+\frac{13}{20}.\frac{19}{20}& \text{Uitwerken } \\ & =-ab+\frac{19}{20}a-\frac{13}{20}b+\frac{247}{400} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-18}{16})(\frac{4}{16}+q)& =(\color{red}{x}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}x-\frac{9}{8}q-\frac{9}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}x-\frac{9}{8}q-\frac{9}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{17}-b)(\frac{-16}{14}-a)& =(\color{red}{-b}+\color{orange}{\frac{7}{17}}).(\color{green}{-a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{7}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{7}b-\frac{7}{17}a-\frac{7}{17}.\frac{8}{7}& \text{Uitwerken } \\ & =ab+\frac{8}{7}b-\frac{7}{17}a-\frac{56}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{8}{7}b-\frac{7}{17}a-\frac{8}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{11}{2})(b+\frac{16}{20})& =(\color{red}{a}+\color{orange}{\frac{-11}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{5}a-\frac{11}{2}b-\frac{11}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =ab+\frac{4}{5}a-\frac{11}{2}b-\frac{44}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{5}a-\frac{11}{2}b-\frac{22}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-13}{5}-b)(\frac{4}{19}+p)& =(\color{red}{-b}+\color{orange}{\frac{-13}{5}}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{19}b-\frac{13}{5}p-\frac{13}{5}.\frac{4}{19}& \text{Uitwerken } \\ & =-bp-\frac{4}{19}b-\frac{13}{5}p-\frac{52}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-5}{7}+p)(x-\frac{-15}{5})& =(\color{red}{p}+\color{orange}{\frac{-5}{7}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3p-\frac{5}{7}x-\frac{5}{7}.3& \text{Uitwerken } \\ & =px+3p-\frac{5}{7}x-\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-5}{14})(\frac{14}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{5}{14}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a-\frac{5}{14}p+\frac{5}{14}.1& \text{Uitwerken } \\ & =-ap+1a-\frac{5}{14}p+\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{5}{16})((-6)-p)& =(\color{red}{x}+\color{orange}{\frac{5}{16}}).(\color{green}{-p}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(\frac{5}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -px-6x-\frac{5}{16}p-\frac{5}{16}.6& \text{Uitwerken } \\ & =-px-6x-\frac{5}{16}p-\frac{30}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-6x-\frac{5}{16}p-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-18 21:44:42
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