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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{9}-x)(b-\frac{-3}{16})& =(\color{red}{-x}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{16}x+\frac{4}{9}b+\frac{4}{9}.\frac{3}{16}& \text{Uitwerken } \\ & =-bx-\frac{3}{16}x+\frac{4}{9}b+\frac{12}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{16}x+\frac{4}{9}b+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{5}{18})(a-\frac{5}{15})& =(\color{red}{x}+\color{orange}{\frac{-5}{18}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x-\frac{5}{18}a+\frac{5}{18}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x-\frac{5}{18}a+\frac{5}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{13}-q)(\frac{-7}{8}-x)& =(\color{red}{-q}+\color{orange}{\frac{-7}{13}}).(\color{green}{-x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{8}q+\frac{7}{13}x+\frac{7}{13}.\frac{7}{8}& \text{Uitwerken } \\ & =qx+\frac{7}{8}q+\frac{7}{13}x+\frac{49}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{19}-a)(\frac{13}{5}+a)& =(\color{red}{-a}+\color{orange}{\frac{-2}{19}}).(\color{green}{a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{5}a-\frac{2}{19}a-\frac{2}{19}.\frac{13}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{5})+(\frac{-2}{19}))a-\frac{26}{95} & \text{Neem samen} \\ &=-a^2-\frac{257}{95}a-\frac{26}{95} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{11}-q)(a+9)& =(\color{red}{-q}+\color{orange}{\frac{-1}{11}}).(\color{green}{a}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(9)} + \color{orange}{(\frac{-1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -aq-9q-\frac{1}{11}a-\frac{1}{11}.9& \text{Uitwerken } \\ & =-aq-9q-\frac{1}{11}a-\frac{9}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{14}{7})(p+\frac{-7}{10})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{10}b-2p+2.\frac{7}{10}& \text{Uitwerken } \\ & =bp-\frac{7}{10}b-2p+\frac{14}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{10}b-2p+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{20}{11})(\frac{3}{10}+a)& =(\color{red}{b}+\color{orange}{\frac{-20}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{10}b-\frac{20}{11}a-\frac{20}{11}.\frac{3}{10}& \text{Uitwerken } \\ & =ab+\frac{3}{10}b-\frac{20}{11}a-\frac{60}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{10}b-\frac{20}{11}a-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{16}+a)(p+2)& =(\color{red}{a}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a-\frac{11}{16}p-\frac{11}{16}.2& \text{Uitwerken } \\ & =ap+2a-\frac{11}{16}p-\frac{22}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+2a-\frac{11}{16}p-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{7}-x)(\frac{-9}{9}-b)& =(\color{red}{-x}+\color{orange}{\frac{5}{7}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-\frac{5}{7}b-\frac{5}{7}.1& \text{Uitwerken } \\ & =bx+1x-\frac{5}{7}b-\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-8}{12})(\frac{6}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{-q}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{6}{19}q-\frac{2}{3}q+\frac{2}{3}.\frac{6}{19}& \text{Uitwerken } \\ & =-q^2+(\frac{6}{19}+(\frac{-2}{3}))q+(\frac{-12}{57}) & \text{Neem samen} \\ &=-q^2-\frac{20}{57}q+(\frac{-12}{57}) & \text{Maak de som} \\ &=-q^2-\frac{20}{57}q+(\frac{-4}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{20}+p)(\frac{9}{2}-x)& =(\color{red}{p}+\color{orange}{\frac{-11}{20}}).(\color{green}{-x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{2}p+\frac{11}{20}x-\frac{11}{20}.\frac{9}{2}& \text{Uitwerken } \\ & =-px+\frac{9}{2}p+\frac{11}{20}x-\frac{99}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{17}+a)(\frac{2}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{-5}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{3}a-\frac{5}{17}p-\frac{5}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =ap+\frac{1}{3}a-\frac{5}{17}p-\frac{5}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-26 04:57:29
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