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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-20}{5})(q+\frac{15}{10})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}x-4q-4.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}x-4q-\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{2}x-4q-6 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{15}-x)(\frac{20}{20}-q)& =(\color{red}{-x}+\color{orange}{\frac{-4}{15}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x+\frac{4}{15}q-\frac{4}{15}.1& \text{Uitwerken } \\ & =qx-1x+\frac{4}{15}q-\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-17}{13})(6-p)& =(\color{red}{p}+\color{orange}{\frac{-17}{13}}).(\color{green}{-p}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(6)} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -pp+6p+\frac{17}{13}p-\frac{17}{13}.6& \text{Uitwerken } \\ & =-p^2+(6+\frac{17}{13})p-\frac{102}{13} & \text{Neem samen} \\ &=-p^2+\frac{95}{13}p-\frac{102}{13} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{19}+b)(\frac{10}{17}+b)& =(\color{red}{b}+\color{orange}{\frac{11}{19}}).(\color{green}{b}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{10}{17}b+\frac{11}{19}b+\frac{11}{19}.\frac{10}{17}& \text{Uitwerken } \\ & =b^2+(\frac{10}{17}+\frac{11}{19})b+\frac{110}{323} & \text{Neem samen} \\ &=b^2+\frac{377}{323}b+\frac{110}{323} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{2}+x)(q-\frac{14}{16})& =(\color{red}{x}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{8}x+\frac{5}{2}q-\frac{5}{2}.\frac{7}{8}& \text{Uitwerken } \\ & =qx-\frac{7}{8}x+\frac{5}{2}q-\frac{35}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{4}-x)(\frac{-7}{4}+a)& =(\color{red}{-x}+\color{orange}{\frac{-11}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{4}x-\frac{11}{4}a+\frac{11}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =-ax+\frac{7}{4}x-\frac{11}{4}a+\frac{77}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{8}{10})(\frac{-14}{10}-p)& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{-p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{5}p+\frac{4}{5}p+\frac{4}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{5})+\frac{4}{5})p+(\frac{-28}{25}) & \text{Neem samen} \\ &=-p^2-\frac{3}{5}p+(\frac{-28}{25}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{9}-x)(\frac{-20}{7}+a)& =(\color{red}{-x}+\color{orange}{\frac{-11}{9}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{7}x-\frac{11}{9}a+\frac{11}{9}.\frac{20}{7}& \text{Uitwerken } \\ & =-ax+\frac{20}{7}x-\frac{11}{9}a+\frac{220}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{9}{4})(\frac{-5}{6}-b)& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{-b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{6}b+\frac{9}{4}b+\frac{9}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{6})+\frac{9}{4})b+(\frac{-45}{24}) & \text{Neem samen} \\ &=-b^2+\frac{17}{12}b+(\frac{-45}{24}) & \text{Maak de som} \\ &=-b^2+\frac{17}{12}b+(\frac{-15}{8}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(16-x)(\frac{18}{17}-b)& =(\color{red}{-x}+\color{orange}{16}).(\color{green}{-b}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(16)} . \color{green}{(-b)} + \color{orange}{(16)} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{17}x-16b+16.\frac{18}{17}& \text{Uitwerken } \\ & =bx-\frac{18}{17}x-16b+\frac{288}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{3}+a)(\frac{7}{9}-q)& =(\color{red}{a}+\color{orange}{\frac{7}{3}}).(\color{green}{-q}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{9}a-\frac{7}{3}q+\frac{7}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =-aq+\frac{7}{9}a-\frac{7}{3}q+\frac{49}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{13}{6})(x+\frac{-2}{2})& =(\color{red}{b}+\color{orange}{\frac{13}{6}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1b+\frac{13}{6}x-\frac{13}{6}.1& \text{Uitwerken } \\ & =bx-1b+\frac{13}{6}x-\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-29 11:10:45
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