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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{4}-p)(p-\frac{11}{3})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{11}{3}p-1p+1.\frac{11}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{11}{3}+(-1))p+(\frac{-11}{3}) & \text{Neem samen} \\ &=-p^2+\frac{8}{3}p+(\frac{-11}{3}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q+\frac{19}{13})(x+6)& =(\color{red}{q}+\color{orange}{\frac{19}{13}}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = qx+6q+\frac{19}{13}x+\frac{19}{13}.6& \text{Uitwerken } \\ & =qx+6q+\frac{19}{13}x+\frac{114}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{8}-q)(q-\frac{-8}{18})& =(\color{red}{-q}+\color{orange}{\frac{5}{8}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{4}{9}q+\frac{5}{8}q+\frac{5}{8}.\frac{4}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-4}{9})+\frac{5}{8})q+(\frac{-20}{72}) & \text{Neem samen} \\ &=-q^2+\frac{13}{72}q+(\frac{-20}{72}) & \text{Maak de som} \\ &=-q^2+\frac{13}{72}q+(\frac{-5}{18}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{18}+a)(\frac{1}{13}-p)& =(\color{red}{a}+\color{orange}{\frac{19}{18}}).(\color{green}{-p}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{19}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{13}a-\frac{19}{18}p+\frac{19}{18}.\frac{1}{13}& \text{Uitwerken } \\ & =-ap+\frac{1}{13}a-\frac{19}{18}p+\frac{19}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-3}{7})(\frac{6}{10}+q)& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{5}a-\frac{3}{7}q-\frac{3}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =aq+\frac{3}{5}a-\frac{3}{7}q-\frac{9}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-3}{16}+a)(b+\frac{6}{12})& =(\color{red}{a}+\color{orange}{\frac{-3}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-\frac{3}{16}b-\frac{3}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-\frac{3}{16}b-\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{9}-p)(\frac{-2}{17}-a)& =(\color{red}{-p}+\color{orange}{\frac{7}{9}}).(\color{green}{-a}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{17}p-\frac{7}{9}a-\frac{7}{9}.\frac{2}{17}& \text{Uitwerken } \\ & =ap+\frac{2}{17}p-\frac{7}{9}a-\frac{14}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{19}-b)(x-\frac{17}{5})& =(\color{red}{-b}+\color{orange}{\frac{-17}{19}}).(\color{green}{x}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{5}b-\frac{17}{19}x+\frac{17}{19}.\frac{17}{5}& \text{Uitwerken } \\ & =-bx+\frac{17}{5}b-\frac{17}{19}x+\frac{289}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{15}+p)(a-\frac{-3}{3})& =(\color{red}{p}+\color{orange}{\frac{7}{15}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{15})} . \color{green}{(a)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p+\frac{7}{15}a+\frac{7}{15}.1& \text{Uitwerken } \\ & =ap+1p+\frac{7}{15}a+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{20}-b)(b-\frac{-6}{11})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{6}{11}b+\frac{3}{4}b+\frac{3}{4}.\frac{6}{11}& \text{Uitwerken } \\ & =-b^2+((\frac{-6}{11})+\frac{3}{4})b+(\frac{-18}{44}) & \text{Neem samen} \\ &=-b^2+\frac{9}{44}b+(\frac{-18}{44}) & \text{Maak de som} \\ &=-b^2+\frac{9}{44}b+(\frac{-9}{22}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-3}{6})(\frac{-9}{3}-b)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3q+\frac{1}{2}b+\frac{1}{2}.3& \text{Uitwerken } \\ & =-bq-3q+\frac{1}{2}b+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{10}+b)(\frac{8}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{15}b+\frac{2}{5}a+\frac{2}{5}.\frac{8}{15}& \text{Uitwerken } \\ & =ab+\frac{8}{15}b+\frac{2}{5}a+\frac{16}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-21 13:02:13
Een site van Busleyden Atheneum Mechelen