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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-9}{5})(\frac{11}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{16}b-\frac{9}{5}a-\frac{9}{5}.\frac{11}{16}& \text{Uitwerken } \\ & =ab+\frac{11}{16}b-\frac{9}{5}a-\frac{99}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{5}{14})(x-\frac{-5}{19})& =(\color{red}{p}+\color{orange}{\frac{-5}{14}}).(\color{green}{x}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{19}p-\frac{5}{14}x-\frac{5}{14}.\frac{5}{19}& \text{Uitwerken } \\ & =px+\frac{5}{19}p-\frac{5}{14}x-\frac{25}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-5}{12})(b+\frac{-20}{16})& =(\color{red}{q}+\color{orange}{\frac{5}{12}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{4}q+\frac{5}{12}b-\frac{5}{12}.\frac{5}{4}& \text{Uitwerken } \\ & =bq-\frac{5}{4}q+\frac{5}{12}b-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{8}-q)(p+\frac{-15}{6})& =(\color{red}{-q}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{2}q-\frac{5}{4}p+\frac{5}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq+\frac{5}{2}q-\frac{5}{4}p+\frac{25}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{8}{10})(b+\frac{3}{14})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{14}p-\frac{4}{5}b-\frac{4}{5}.\frac{3}{14}& \text{Uitwerken } \\ & =bp+\frac{3}{14}p-\frac{4}{5}b-\frac{12}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{14}p-\frac{4}{5}b-\frac{6}{35} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{20}+b)(\frac{12}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{-9}{20}}).(\color{green}{-q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}b+\frac{9}{20}q-\frac{9}{20}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}b+\frac{9}{20}q-\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{7}{14})(\frac{19}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{7}p-\frac{1}{2}a-\frac{1}{2}.\frac{19}{7}& \text{Uitwerken } \\ & =ap+\frac{19}{7}p-\frac{1}{2}a-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{11}{20})(\frac{-17}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{-11}{20}}).(\color{green}{-p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{17}{4}x+\frac{11}{20}p+\frac{11}{20}.\frac{17}{4}& \text{Uitwerken } \\ & =-px-\frac{17}{4}x+\frac{11}{20}p+\frac{187}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-9}{19})(\frac{-6}{7}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{19}}).(\color{green}{-q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{7}b-\frac{9}{19}q-\frac{9}{19}.\frac{6}{7}& \text{Uitwerken } \\ & =-bq-\frac{6}{7}b-\frac{9}{19}q-\frac{54}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-13}{16})(\frac{-12}{17}+a)& =(\color{red}{p}+\color{orange}{\frac{13}{16}}).(\color{green}{a}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{12}{17}p+\frac{13}{16}a-\frac{13}{16}.\frac{12}{17}& \text{Uitwerken } \\ & =ap-\frac{12}{17}p+\frac{13}{16}a-\frac{156}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{12}{17}p+\frac{13}{16}a-\frac{39}{68} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{5}{6})(q+\frac{5}{8})& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{8}x-\frac{5}{6}q-\frac{5}{6}.\frac{5}{8}& \text{Uitwerken } \\ & =qx+\frac{5}{8}x-\frac{5}{6}q-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{14}-p)(\frac{15}{14}+p)& =(\color{red}{-p}+\color{orange}{\frac{9}{14}}).(\color{green}{p}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{9}{14})} . \color{green}{(p)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{15}{14}p+\frac{9}{14}p+\frac{9}{14}.\frac{15}{14}& \text{Uitwerken } \\ & =-p^2+((\frac{-15}{14})+\frac{9}{14})p+(\frac{-135}{196}) & \text{Neem samen} \\ &=-p^2-\frac{6}{14}p+(\frac{-135}{196}) & \text{Maak de som} \\ &=-p^2-\frac{3}{7}p+(\frac{-135}{196}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-03 15:28:17
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