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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-4}{8})(\frac{4}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{1}{2}a-\frac{1}{2}.1& \text{Uitwerken } \\ & =ap+1p-\frac{1}{2}a-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{16}+x)(p-\frac{1}{12})& =(\color{red}{x}+\color{orange}{\frac{-9}{16}}).(\color{green}{p}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{12}x-\frac{9}{16}p+\frac{9}{16}.\frac{1}{12}& \text{Uitwerken } \\ & =px-\frac{1}{12}x-\frac{9}{16}p+\frac{9}{192} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{12}x-\frac{9}{16}p+\frac{3}{64} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{7}+a)(\frac{7}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{-11}{7}}).(\color{green}{-a}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{15}a+\frac{11}{7}a-\frac{11}{7}.\frac{7}{15}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{15}+\frac{11}{7})a-\frac{77}{105} & \text{Neem samen} \\ &=-a^2+\frac{214}{105}a-\frac{77}{105} & \text{Maak de som} \\ &=-a^2+\frac{214}{105}a-\frac{11}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-14}{8})(\frac{-12}{6}+q)& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2a-\frac{7}{4}q+\frac{7}{4}.2& \text{Uitwerken } \\ & =aq-2a-\frac{7}{4}q+\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-2a-\frac{7}{4}q+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{13}-x)(b-\frac{-15}{18})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{6}x+1b+1.\frac{5}{6}& \text{Uitwerken } \\ & =-bx-\frac{5}{6}x+1b+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{9}+q)(\frac{-11}{13}+q)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{13}q+\frac{2}{3}q-\frac{2}{3}.\frac{11}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{13})+\frac{2}{3})q-(\frac{-22}{39}) & \text{Neem samen} \\ &=q^2-\frac{7}{39}q-(\frac{-22}{39}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-20}{3})(p+\frac{-6}{20})& =(\color{red}{q}+\color{orange}{\frac{-20}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{10}q-\frac{20}{3}p+\frac{20}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =pq-\frac{3}{10}q-\frac{20}{3}p+\frac{60}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{10}q-\frac{20}{3}p+2 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-4}{15})(\frac{-16}{17}-q)& =(\color{red}{x}+\color{orange}{\frac{-4}{15}}).(\color{green}{-q}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{17}x+\frac{4}{15}q+\frac{4}{15}.\frac{16}{17}& \text{Uitwerken } \\ & =-qx-\frac{16}{17}x+\frac{4}{15}q+\frac{64}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-20)-b)(b+\frac{2}{19})& =(\color{red}{-b}+\color{orange}{(-20)}).(\color{green}{b}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(-20)} . \color{green}{(b)} + \color{orange}{(-20)} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{2}{19}b-20b-20.\frac{2}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-2}{19})+(-20))b-\frac{40}{19} & \text{Neem samen} \\ &=-b^2-\frac{382}{19}b-\frac{40}{19} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{3}-b)(\frac{19}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{-p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{15}b-\frac{1}{3}p+\frac{1}{3}.\frac{19}{15}& \text{Uitwerken } \\ & =bp-\frac{19}{15}b-\frac{1}{3}p+\frac{19}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{17}{4})(\frac{20}{11}+x)& =(\color{red}{x}+\color{orange}{\frac{-17}{4}}).(\color{green}{x}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{20}{11}x-\frac{17}{4}x-\frac{17}{4}.\frac{20}{11}& \text{Uitwerken } \\ & =x^2+(\frac{20}{11}+(\frac{-17}{4}))x-(\frac{-340}{44}) & \text{Neem samen} \\ &=x^2-\frac{107}{44}x-(\frac{-340}{44}) & \text{Maak de som} \\ &=x^2-\frac{107}{44}x+\frac{85}{11} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(q-7)(\frac{1}{2}-a)& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-7)} . \color{green}{(-a)} + \color{orange}{(-7)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}q+7a-7.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}q+7a-\frac{7}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-18 06:12:51
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