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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{15}-b)(\frac{3}{13}-x)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{13}b+1x-1.\frac{3}{13}& \text{Uitwerken } \\ & =bx-\frac{3}{13}b+1x-\frac{3}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{10}+q)(\frac{-4}{18}+a)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{9}q+2a-2.\frac{2}{9}& \text{Uitwerken } \\ & =aq-\frac{2}{9}q+2a-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{20}+q)(\frac{-11}{6}+q)& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{6}q-\frac{7}{10}q+\frac{7}{10}.\frac{11}{6}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{6})+(\frac{-7}{10}))q+\frac{77}{60} & \text{Neem samen} \\ &=q^2-\frac{76}{30}q+\frac{77}{60} & \text{Maak de som} \\ &=q^2-\frac{38}{15}q+\frac{77}{60} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{8}+a)(b-\frac{6}{20})& =(\color{red}{a}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{10}a+\frac{11}{8}b-\frac{11}{8}.\frac{3}{10}& \text{Uitwerken } \\ & =ab-\frac{3}{10}a+\frac{11}{8}b-\frac{33}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-9}{14})(x-\frac{11}{7})& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{x}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{9}{14})} . \color{green}{(x)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{7}p+\frac{9}{14}x-\frac{9}{14}.\frac{11}{7}& \text{Uitwerken } \\ & =px-\frac{11}{7}p+\frac{9}{14}x-\frac{99}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-6}{12}+x)(x-\frac{-19}{4})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{4}x-\frac{1}{2}x-\frac{1}{2}.\frac{19}{4}& \text{Uitwerken } \\ & =x^2+(\frac{19}{4}+(\frac{-1}{2}))x-(\frac{-19}{8}) & \text{Neem samen} \\ &=x^2+\frac{17}{4}x-(\frac{-19}{8}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(a+\frac{6}{20})(q+\frac{11}{15})& =(\color{red}{a}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{15}a+\frac{3}{10}q+\frac{3}{10}.\frac{11}{15}& \text{Uitwerken } \\ & =aq+\frac{11}{15}a+\frac{3}{10}q+\frac{33}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{11}{15}a+\frac{3}{10}q+\frac{11}{50} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{6}{12})(a-\frac{20}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{17}p+\frac{1}{2}a-\frac{1}{2}.\frac{20}{17}& \text{Uitwerken } \\ & =ap-\frac{20}{17}p+\frac{1}{2}a-\frac{20}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{20}{17}p+\frac{1}{2}a-\frac{10}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{18}-b)(p-\frac{-20}{17})& =(\color{red}{-b}+\color{orange}{\frac{5}{18}}).(\color{green}{p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{17}b+\frac{5}{18}p+\frac{5}{18}.\frac{20}{17}& \text{Uitwerken } \\ & =-bp-\frac{20}{17}b+\frac{5}{18}p+\frac{100}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{17}b+\frac{5}{18}p+\frac{50}{153} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{2}{7})(\frac{-8}{20}-a)& =(\color{red}{q}+\color{orange}{\frac{2}{7}}).(\color{green}{-a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{5}q-\frac{2}{7}a-\frac{2}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =-aq-\frac{2}{5}q-\frac{2}{7}a-\frac{4}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{2}+b)(\frac{17}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{13}{2}}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{16}b+\frac{13}{2}p+\frac{13}{2}.\frac{17}{16}& \text{Uitwerken } \\ & =bp+\frac{17}{16}b+\frac{13}{2}p+\frac{221}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{18}-x)(\frac{-13}{13}-b)& =(\color{red}{-x}+\color{orange}{\frac{-1}{6}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+\frac{1}{6}b+\frac{1}{6}.1& \text{Uitwerken } \\ & =bx+1x+\frac{1}{6}b+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-04 23:15:45
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