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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-4}{8})(x+\frac{-15}{15})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a-\frac{1}{2}x+\frac{1}{2}.1& \text{Uitwerken } \\ & =ax-1a-\frac{1}{2}x+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{4}{16})(\frac{8}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x-\frac{1}{4}a-\frac{1}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x-\frac{1}{4}a-\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x-\frac{1}{4}a-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-20}{14})(x+\frac{4}{5})& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}q+\frac{10}{7}x+\frac{10}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}q+\frac{10}{7}x+\frac{40}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{5}q+\frac{10}{7}x+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{1}{12})(q+\frac{-18}{12})& =(\color{red}{x}+\color{orange}{\frac{1}{12}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{2}x+\frac{1}{12}q-\frac{1}{12}.\frac{3}{2}& \text{Uitwerken } \\ & =qx-\frac{3}{2}x+\frac{1}{12}q-\frac{3}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{2}x+\frac{1}{12}q-\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{17}+x)(q-\frac{-12}{16})& =(\color{red}{x}+\color{orange}{\frac{-8}{17}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{4}x-\frac{8}{17}q-\frac{8}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =qx+\frac{3}{4}x-\frac{8}{17}q-\frac{24}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{4}x-\frac{8}{17}q-\frac{6}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{18}-a)(\frac{12}{17}-q)& =(\color{red}{-a}+\color{orange}{\frac{17}{18}}).(\color{green}{-q}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{17}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{17}a-\frac{17}{18}q+\frac{17}{18}.\frac{12}{17}& \text{Uitwerken } \\ & =aq-\frac{12}{17}a-\frac{17}{18}q+\frac{204}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{12}{17}a-\frac{17}{18}q+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a-\frac{17}{10})(x+\frac{-5}{14})& =(\color{red}{a}+\color{orange}{\frac{-17}{10}}).(\color{green}{x}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{14}a-\frac{17}{10}x+\frac{17}{10}.\frac{5}{14}& \text{Uitwerken } \\ & =ax-\frac{5}{14}a-\frac{17}{10}x+\frac{85}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{14}a-\frac{17}{10}x+\frac{17}{28} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{6}{4})(p+\frac{1}{14})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{14}b-\frac{3}{2}p-\frac{3}{2}.\frac{1}{14}& \text{Uitwerken } \\ & =bp+\frac{1}{14}b-\frac{3}{2}p-\frac{3}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{18}{20})(\frac{-4}{7}+b)& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{7}q+\frac{9}{10}b-\frac{9}{10}.\frac{4}{7}& \text{Uitwerken } \\ & =bq-\frac{4}{7}q+\frac{9}{10}b-\frac{36}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{4}{7}q+\frac{9}{10}b-\frac{18}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+\frac{-15}{18})(q+\frac{-6}{20})& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{10}a-\frac{5}{6}q+\frac{5}{6}.\frac{3}{10}& \text{Uitwerken } \\ & =aq-\frac{3}{10}a-\frac{5}{6}q+\frac{15}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{10}a-\frac{5}{6}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{2}{20})(p+\frac{7}{20})& =(\color{red}{x}+\color{orange}{\frac{1}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{20}x+\frac{1}{10}p+\frac{1}{10}.\frac{7}{20}& \text{Uitwerken } \\ & =px+\frac{7}{20}x+\frac{1}{10}p+\frac{7}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{4}-p)(\frac{-17}{6}+b)& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{6}p-\frac{1}{2}b+\frac{1}{2}.\frac{17}{6}& \text{Uitwerken } \\ & =-bp+\frac{17}{6}p-\frac{1}{2}b+\frac{17}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-07 04:50:38
Een site van Busleyden Atheneum Mechelen