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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{9}{19})(a+\frac{10}{2})& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = aq+5q+\frac{9}{19}a+\frac{9}{19}.5& \text{Uitwerken } \\ & =aq+5q+\frac{9}{19}a+\frac{45}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-20}{4})(\frac{-15}{12}-x)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{-x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(-5)} . \color{green}{(-x)} + \color{orange}{(-5)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{4}p+5x+5.\frac{5}{4}& \text{Uitwerken } \\ & =-px-\frac{5}{4}p+5x+\frac{25}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{16}-p)(\frac{5}{5}-b)& =(\color{red}{-p}+\color{orange}{\frac{1}{16}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{1}{16}b+\frac{1}{16}.1& \text{Uitwerken } \\ & =bp-1p-\frac{1}{16}b+\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{2}{16})(p+\frac{-18}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{5}x-\frac{1}{8}p+\frac{1}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =px-\frac{6}{5}x-\frac{1}{8}p+\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{6}{5}x-\frac{1}{8}p+\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-17}{12}-p)(\frac{-11}{17}+q)& =(\color{red}{-p}+\color{orange}{\frac{-17}{12}}).(\color{green}{q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{17}p-\frac{17}{12}q+\frac{17}{12}.\frac{11}{17}& \text{Uitwerken } \\ & =-pq+\frac{11}{17}p-\frac{17}{12}q+\frac{187}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{11}{17}p-\frac{17}{12}q+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{12}+b)(\frac{13}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{-b}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{18}b-\frac{3}{2}b+\frac{3}{2}.\frac{13}{18}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{18}+(\frac{-3}{2}))b+(\frac{-39}{36}) & \text{Neem samen} \\ &=-b^2-\frac{14}{18}b+(\frac{-39}{36}) & \text{Maak de som} \\ &=-b^2-\frac{7}{9}b+(\frac{-13}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-7}{8})(\frac{-17}{2}-b)& =(\color{red}{p}+\color{orange}{\frac{-7}{8}}).(\color{green}{-b}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{2}p+\frac{7}{8}b+\frac{7}{8}.\frac{17}{2}& \text{Uitwerken } \\ & =-bp-\frac{17}{2}p+\frac{7}{8}b+\frac{119}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-1}{6})(\frac{-18}{12}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p+\frac{1}{6}a-\frac{1}{6}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p+\frac{1}{6}a-\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{2}p+\frac{1}{6}a-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-13}{3})(a-\frac{-19}{10})& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{10}x+\frac{13}{3}a+\frac{13}{3}.\frac{19}{10}& \text{Uitwerken } \\ & =ax+\frac{19}{10}x+\frac{13}{3}a+\frac{247}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{2}-x)(x+\frac{12}{2})& =(\color{red}{-x}+\color{orange}{7}).(\color{green}{x}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(6)} + \color{orange}{(7)} . \color{green}{(x)} + \color{orange}{(7)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -xx-6x+7x+7.6& \text{Uitwerken } \\ & =-x^2+((-6)+7)x+(-42) & \text{Neem samen} \\ &=-x^2+1x+(-42) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-8}{9})(\frac{4}{2}+x)& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p-\frac{8}{9}x-\frac{8}{9}.2& \text{Uitwerken } \\ & =px+2p-\frac{8}{9}x-\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{13}+a)(a+\frac{14}{6})& =(\color{red}{a}+\color{orange}{\frac{10}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{3}a+\frac{10}{13}a+\frac{10}{13}.\frac{7}{3}& \text{Uitwerken } \\ & =a^2+(\frac{7}{3}+\frac{10}{13})a+\frac{70}{39} & \text{Neem samen} \\ &=a^2+\frac{121}{39}a+\frac{70}{39} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-15 14:24:51
Een site van Busleyden Atheneum Mechelen