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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{19}{3})(q+\frac{-5}{16})& =(\color{red}{a}+\color{orange}{\frac{-19}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{16}a-\frac{19}{3}q+\frac{19}{3}.\frac{5}{16}& \text{Uitwerken } \\ & =aq-\frac{5}{16}a-\frac{19}{3}q+\frac{95}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-20}{20})(\frac{-1}{15}-b)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{15}q-1b-1.\frac{1}{15}& \text{Uitwerken } \\ & =-bq-\frac{1}{15}q-1b-\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}((-12)+p)(a-\frac{-3}{7})& =(\color{red}{p}+\color{orange}{(-12)}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(-12)} . \color{green}{(a)} + \color{orange}{(-12)} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{7}p-12a-12.\frac{3}{7}& \text{Uitwerken } \\ & =ap+\frac{3}{7}p-12a-\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{8}+a)(\frac{-14}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{-p}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{15}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{14}{9}a-\frac{15}{8}p-\frac{15}{8}.\frac{14}{9}& \text{Uitwerken } \\ & =-ap-\frac{14}{9}a-\frac{15}{8}p-\frac{210}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{14}{9}a-\frac{15}{8}p-\frac{35}{12} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{5}{10})(\frac{16}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{-p}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{16}{11}p+\frac{1}{2}p-\frac{1}{2}.\frac{16}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{16}{11}+\frac{1}{2})p-\frac{16}{22} & \text{Neem samen} \\ &=-p^2+\frac{43}{22}p-\frac{16}{22} & \text{Maak de som} \\ &=-p^2+\frac{43}{22}p-\frac{8}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}((-1)+b)(\frac{9}{5}-p)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{5}b+1p-1.\frac{9}{5}& \text{Uitwerken } \\ & =-bp+\frac{9}{5}b+1p-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{15}-q)(x-\frac{-8}{4})& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2q+\frac{2}{3}x+\frac{2}{3}.2& \text{Uitwerken } \\ & =-qx-2q+\frac{2}{3}x+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{9}+b)(\frac{-16}{8}-a)& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab-2b+\frac{1}{3}a+\frac{1}{3}.2& \text{Uitwerken } \\ & =-ab-2b+\frac{1}{3}a+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-13}{8})(\frac{-4}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{13}{8}}).(\color{green}{-x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{13}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{7}a-\frac{13}{8}x-\frac{13}{8}.\frac{4}{7}& \text{Uitwerken } \\ & =-ax-\frac{4}{7}a-\frac{13}{8}x-\frac{52}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{4}{7}a-\frac{13}{8}x-\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{20}+b)(a+\frac{14}{18})& =(\color{red}{b}+\color{orange}{\frac{-7}{20}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{9}b-\frac{7}{20}a-\frac{7}{20}.\frac{7}{9}& \text{Uitwerken } \\ & =ab+\frac{7}{9}b-\frac{7}{20}a-\frac{49}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}((-5)+a)(\frac{-5}{2}-b)& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{-b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(-5)} . \color{green}{(-b)} + \color{orange}{(-5)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{2}a+5b+5.\frac{5}{2}& \text{Uitwerken } \\ & =-ab-\frac{5}{2}a+5b+\frac{25}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{17}{16})(p-\frac{11}{11})& =(\color{red}{p}+\color{orange}{\frac{17}{16}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p+\frac{17}{16}p-\frac{17}{16}.1& \text{Uitwerken } \\ & =p^2+((-1)+\frac{17}{16})p-(\frac{-17}{16}) & \text{Neem samen} \\ &=p^2+\frac{1}{16}p-(\frac{-17}{16}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 04:39:51