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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-9}{17})(x-\frac{-15}{5})& =(\color{red}{p}+\color{orange}{\frac{-9}{17}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3p-\frac{9}{17}x-\frac{9}{17}.3& \text{Uitwerken } \\ & =px+3p-\frac{9}{17}x-\frac{27}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-19}{14})(\frac{-13}{3}+q)& =(\color{red}{a}+\color{orange}{\frac{19}{14}}).(\color{green}{q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{3}a+\frac{19}{14}q-\frac{19}{14}.\frac{13}{3}& \text{Uitwerken } \\ & =aq-\frac{13}{3}a+\frac{19}{14}q-\frac{247}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{15}+x)(q+\frac{-7}{3})& =(\color{red}{x}+\color{orange}{\frac{-4}{15}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{3}x-\frac{4}{15}q+\frac{4}{15}.\frac{7}{3}& \text{Uitwerken } \\ & =qx-\frac{7}{3}x-\frac{4}{15}q+\frac{28}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{2}{14})(b-\frac{13}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{15}x-\frac{1}{7}b+\frac{1}{7}.\frac{13}{15}& \text{Uitwerken } \\ & =bx-\frac{13}{15}x-\frac{1}{7}b+\frac{13}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{10}{19})(\frac{5}{19}-x)& =(\color{red}{b}+\color{orange}{\frac{10}{19}}).(\color{green}{-x}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{10}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{19}b-\frac{10}{19}x+\frac{10}{19}.\frac{5}{19}& \text{Uitwerken } \\ & =-bx+\frac{5}{19}b-\frac{10}{19}x+\frac{50}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-3}{8}+a)(\frac{-15}{3}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{-p}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ap-5a+\frac{3}{8}p+\frac{3}{8}.5& \text{Uitwerken } \\ & =-ap-5a+\frac{3}{8}p+\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{12}-x)(b-\frac{-1}{13})& =(\color{red}{-x}+\color{orange}{\frac{1}{12}}).(\color{green}{b}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{1}{12})} . \color{green}{(b)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{13}x+\frac{1}{12}b+\frac{1}{12}.\frac{1}{13}& \text{Uitwerken } \\ & =-bx-\frac{1}{13}x+\frac{1}{12}b+\frac{1}{156} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{15}-a)(p-\frac{14}{16})& =(\color{red}{-a}+\color{orange}{\frac{6}{5}}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{8}a+\frac{6}{5}p-\frac{6}{5}.\frac{7}{8}& \text{Uitwerken } \\ & =-ap+\frac{7}{8}a+\frac{6}{5}p-\frac{42}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{7}{8}a+\frac{6}{5}p-\frac{21}{20} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}((-18)+x)(p-\frac{13}{11})& =(\color{red}{x}+\color{orange}{(-18)}).(\color{green}{p}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(-18)} . \color{green}{(p)} + \color{orange}{(-18)} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{11}x-18p+18.\frac{13}{11}& \text{Uitwerken } \\ & =px-\frac{13}{11}x-18p+\frac{234}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{14}-a)(a-\frac{-9}{4})& =(\color{red}{-a}+\color{orange}{\frac{-3}{14}}).(\color{green}{a}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{4}a-\frac{3}{14}a-\frac{3}{14}.\frac{9}{4}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{4})+(\frac{-3}{14}))a-\frac{27}{56} & \text{Neem samen} \\ &=-a^2-\frac{69}{28}a-\frac{27}{56} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{7}-p)((-6)+p)& =(\color{red}{-p}+\color{orange}{\frac{2}{7}}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-6)} + \color{orange}{(\frac{2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -pp+6p+\frac{2}{7}p-\frac{2}{7}.6& \text{Uitwerken } \\ & =-p^2+(6+\frac{2}{7})p-\frac{12}{7} & \text{Neem samen} \\ &=-p^2+\frac{44}{7}p-\frac{12}{7} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{20}+b)(\frac{-17}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{-9}{10}}).(\color{green}{q}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{15}b-\frac{9}{10}q+\frac{9}{10}.\frac{17}{15}& \text{Uitwerken } \\ & =bq-\frac{17}{15}b-\frac{9}{10}q+\frac{153}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{17}{15}b-\frac{9}{10}q+\frac{51}{50} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-23 16:15:28
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