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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{8}{8})(p+\frac{-15}{4})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{4}a-1p+1.\frac{15}{4}& \text{Uitwerken } \\ & =ap-\frac{15}{4}a-1p+\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{10}{20})(\frac{-5}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{19}b+\frac{1}{2}a-\frac{1}{2}.\frac{5}{19}& \text{Uitwerken } \\ & =ab-\frac{5}{19}b+\frac{1}{2}a-\frac{5}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{14}+b)(\frac{-3}{12}+b)& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{4}b-\frac{5}{7}b+\frac{5}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{4})+(\frac{-5}{7}))b+\frac{5}{28} & \text{Neem samen} \\ &=b^2-\frac{27}{28}b+\frac{5}{28} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x+\frac{19}{10})(a-\frac{-3}{3})& =(\color{red}{x}+\color{orange}{\frac{19}{10}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{10})} . \color{green}{(a)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x+\frac{19}{10}a+\frac{19}{10}.1& \text{Uitwerken } \\ & =ax+1x+\frac{19}{10}a+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{12}-a)((-6)-p)& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(-6)} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ap+6a-\frac{1}{3}p-\frac{1}{3}.6& \text{Uitwerken } \\ & =ap+6a-\frac{1}{3}p-\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+6a-\frac{1}{3}p-2 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-13}{17})(q+\frac{15}{8})& =(\color{red}{b}+\color{orange}{\frac{13}{17}}).(\color{green}{q}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{8}b+\frac{13}{17}q+\frac{13}{17}.\frac{15}{8}& \text{Uitwerken } \\ & =bq+\frac{15}{8}b+\frac{13}{17}q+\frac{195}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{13}{17})(\frac{-9}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{-13}{17}}).(\color{green}{-a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{5}a+\frac{13}{17}a+\frac{13}{17}.\frac{9}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{5})+\frac{13}{17})a+(\frac{-117}{85}) & \text{Neem samen} \\ &=-a^2-\frac{88}{85}a+(\frac{-117}{85}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x+\frac{1}{5})(\frac{17}{4}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{4}x+\frac{1}{5}p+\frac{1}{5}.\frac{17}{4}& \text{Uitwerken } \\ & =px+\frac{17}{4}x+\frac{1}{5}p+\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-14}{3})(\frac{2}{3}-a)& =(\color{red}{x}+\color{orange}{\frac{14}{3}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{14}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{3}x-\frac{14}{3}a+\frac{14}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax+\frac{2}{3}x-\frac{14}{3}a+\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{16}{7})(b-\frac{20}{14})& =(\color{red}{p}+\color{orange}{\frac{-16}{7}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{7}p-\frac{16}{7}b+\frac{16}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =bp-\frac{10}{7}p-\frac{16}{7}b+\frac{160}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{18}{6}-p)(\frac{-11}{19}-b)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{19}p-3b-3.\frac{11}{19}& \text{Uitwerken } \\ & =bp+\frac{11}{19}p-3b-\frac{33}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{10}{18})(x-\frac{16}{19})& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{19}q+\frac{5}{9}x-\frac{5}{9}.\frac{16}{19}& \text{Uitwerken } \\ & =qx-\frac{16}{19}q+\frac{5}{9}x-\frac{80}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-20 02:07:26
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