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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{20}{9})(p-\frac{-1}{12})& =(\color{red}{x}+\color{orange}{\frac{20}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{20}{9})} . \color{green}{(p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{12}x+\frac{20}{9}p+\frac{20}{9}.\frac{1}{12}& \text{Uitwerken } \\ & =px+\frac{1}{12}x+\frac{20}{9}p+\frac{20}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{12}x+\frac{20}{9}p+\frac{5}{27} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{6}{14})(b-\frac{3}{4})& =(\color{red}{b}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{4}b-\frac{3}{7}b+\frac{3}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{4})+(\frac{-3}{7}))b+\frac{9}{28} & \text{Neem samen} \\ &=b^2-\frac{33}{28}b+\frac{9}{28} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{6}-b)(a+\frac{5}{8})& =(\color{red}{-b}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{8}b-\frac{10}{3}a-\frac{10}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =-ab-\frac{5}{8}b-\frac{10}{3}a-\frac{50}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{5}{8}b-\frac{10}{3}a-\frac{25}{12} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{5}-q)(a-\frac{-12}{16})& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{4}q-1a-1.\frac{3}{4}& \text{Uitwerken } \\ & =-aq-\frac{3}{4}q-1a-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{19}{14})(q-\frac{1}{2})& =(\color{red}{q}+\color{orange}{\frac{-19}{14}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q-\frac{19}{14}q+\frac{19}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+(\frac{-19}{14}))q+\frac{19}{28} & \text{Neem samen} \\ &=q^2-\frac{26}{14}q+\frac{19}{28} & \text{Maak de som} \\ &=q^2-\frac{13}{7}q+\frac{19}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-1}{14})(b-\frac{-17}{18})& =(\color{red}{x}+\color{orange}{\frac{-1}{14}}).(\color{green}{b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{18}x-\frac{1}{14}b-\frac{1}{14}.\frac{17}{18}& \text{Uitwerken } \\ & =bx+\frac{17}{18}x-\frac{1}{14}b-\frac{17}{252} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{13}{9})(\frac{17}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{-q}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{9}b+\frac{13}{9}q-\frac{13}{9}.\frac{17}{9}& \text{Uitwerken } \\ & =-bq+\frac{17}{9}b+\frac{13}{9}q-\frac{221}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{5}{4})(\frac{2}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{2}a+\frac{5}{4}q+\frac{5}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =aq+\frac{1}{2}a+\frac{5}{4}q+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{5}+a)(\frac{18}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{18}{7}a+\frac{3}{5}q-\frac{3}{5}.\frac{18}{7}& \text{Uitwerken } \\ & =-aq+\frac{18}{7}a+\frac{3}{5}q-\frac{54}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{20}+b)(b-\frac{-5}{13})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{13}b-1b-1.\frac{5}{13}& \text{Uitwerken } \\ & =b^2+(\frac{5}{13}+(-1))b-(\frac{-5}{13}) & \text{Neem samen} \\ &=b^2-\frac{8}{13}b-(\frac{-5}{13}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{12}{4})(x+\frac{-8}{9})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{9}a-3x+3.\frac{8}{9}& \text{Uitwerken } \\ & =ax-\frac{8}{9}a-3x+\frac{24}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{8}{9}a-3x+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}((-12)-p)(a-\frac{-15}{20})& =(\color{red}{-p}+\color{orange}{(-12)}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-12)} . \color{green}{(a)} + \color{orange}{(-12)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{4}p-12a-12.\frac{3}{4}& \text{Uitwerken } \\ & =-ap-\frac{3}{4}p-12a-\frac{36}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{4}p-12a-9 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-21 15:54:49
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