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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{18}+b)(\frac{1}{14}-q)& =(\color{red}{b}+\color{orange}{\frac{-13}{18}}).(\color{green}{-q}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{14}b+\frac{13}{18}q-\frac{13}{18}.\frac{1}{14}& \text{Uitwerken } \\ & =-bq+\frac{1}{14}b+\frac{13}{18}q-\frac{13}{252} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{14}-a)(q-\frac{-3}{4})& =(\color{red}{-a}+\color{orange}{\frac{6}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{4}a+\frac{6}{7}q+\frac{6}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-aq-\frac{3}{4}a+\frac{6}{7}q+\frac{18}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{4}a+\frac{6}{7}q+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-15}{20})(\frac{-3}{6}+x)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{2}p+\frac{3}{4}x-\frac{3}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =px-\frac{1}{2}p+\frac{3}{4}x-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{6}-x)(p+\frac{-11}{19})& =(\color{red}{-x}+\color{orange}{\frac{10}{3}}).(\color{green}{p}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{11}{19}x+\frac{10}{3}p-\frac{10}{3}.\frac{11}{19}& \text{Uitwerken } \\ & =-px+\frac{11}{19}x+\frac{10}{3}p-\frac{110}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{15}+a)(\frac{-9}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{-q}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{14}a+\frac{1}{5}q+\frac{1}{5}.\frac{9}{14}& \text{Uitwerken } \\ & =-aq-\frac{9}{14}a+\frac{1}{5}q+\frac{9}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{16}{17})(a+\frac{-5}{19})& =(\color{red}{b}+\color{orange}{\frac{-16}{17}}).(\color{green}{a}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{19}b-\frac{16}{17}a+\frac{16}{17}.\frac{5}{19}& \text{Uitwerken } \\ & =ab-\frac{5}{19}b-\frac{16}{17}a+\frac{80}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{11}-q)(b+\frac{-13}{2})& =(\color{red}{-q}+\color{orange}{\frac{-10}{11}}).(\color{green}{b}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{2}q-\frac{10}{11}b+\frac{10}{11}.\frac{13}{2}& \text{Uitwerken } \\ & =-bq+\frac{13}{2}q-\frac{10}{11}b+\frac{130}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{13}{2}q-\frac{10}{11}b+\frac{65}{11} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-10}{6})(a+\frac{-14}{11})& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{11}x+\frac{5}{3}a-\frac{5}{3}.\frac{14}{11}& \text{Uitwerken } \\ & =ax-\frac{14}{11}x+\frac{5}{3}a-\frac{70}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{6}+q)(\frac{12}{11}+p)& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{12}{11}q-\frac{5}{2}p-\frac{5}{2}.\frac{12}{11}& \text{Uitwerken } \\ & =pq+\frac{12}{11}q-\frac{5}{2}p-\frac{60}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{12}{11}q-\frac{5}{2}p-\frac{30}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{17}{12})(a+\frac{-15}{2})& =(\color{red}{b}+\color{orange}{\frac{-17}{12}}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{2}b-\frac{17}{12}a+\frac{17}{12}.\frac{15}{2}& \text{Uitwerken } \\ & =ab-\frac{15}{2}b-\frac{17}{12}a+\frac{255}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{2}b-\frac{17}{12}a+\frac{85}{8} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-12}{14})(x-\frac{-4}{11})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{x}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{11}q-\frac{6}{7}x-\frac{6}{7}.\frac{4}{11}& \text{Uitwerken } \\ & =qx+\frac{4}{11}q-\frac{6}{7}x-\frac{24}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(4+a)(\frac{10}{15}+q)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{3}a+4q+4.\frac{2}{3}& \text{Uitwerken } \\ & =aq+\frac{2}{3}a+4q+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-04-14 10:01:34