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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{1}{8})(\frac{-13}{18}-x)& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{-x}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{18}b+\frac{1}{8}x+\frac{1}{8}.\frac{13}{18}& \text{Uitwerken } \\ & =-bx-\frac{13}{18}b+\frac{1}{8}x+\frac{13}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}((-4)-a)(x+\frac{15}{8})& =(\color{red}{-a}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{8}a-4x-4.\frac{15}{8}& \text{Uitwerken } \\ & =-ax-\frac{15}{8}a-4x-\frac{60}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{15}{8}a-4x-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-7}{14})(a-\frac{-2}{18})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{9}p+\frac{1}{2}a+\frac{1}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =ap+\frac{1}{9}p+\frac{1}{2}a+\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-2}{4})(\frac{8}{6}+q)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}p+\frac{1}{2}q+\frac{1}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}p+\frac{1}{2}q+\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{3}p+\frac{1}{2}q+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{20}+x)(\frac{-13}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{-q}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{12}x-\frac{4}{5}q-\frac{4}{5}.\frac{13}{12}& \text{Uitwerken } \\ & =-qx-\frac{13}{12}x-\frac{4}{5}q-\frac{52}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{13}{12}x-\frac{4}{5}q-\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(5-p)(x-\frac{20}{18})& =(\color{red}{-p}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{9}p+5x-5.\frac{10}{9}& \text{Uitwerken } \\ & =-px+\frac{10}{9}p+5x-\frac{50}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-18}{16})(b-\frac{-6}{13})& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{6}{13}p+\frac{9}{8}b+\frac{9}{8}.\frac{6}{13}& \text{Uitwerken } \\ & =bp+\frac{6}{13}p+\frac{9}{8}b+\frac{54}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{6}{13}p+\frac{9}{8}b+\frac{27}{52} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-2}{20})(\frac{-20}{15}+b)& =(\color{red}{b}+\color{orange}{\frac{-1}{10}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{4}{3}b-\frac{1}{10}b+\frac{1}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-4}{3})+(\frac{-1}{10}))b+\frac{4}{30} & \text{Neem samen} \\ &=b^2-\frac{43}{30}b+\frac{4}{30} & \text{Maak de som} \\ &=b^2-\frac{43}{30}b+\frac{2}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{18}-b)(x+\frac{10}{18})& =(\color{red}{-b}+\color{orange}{\frac{-1}{18}}).(\color{green}{x}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{9}b-\frac{1}{18}x-\frac{1}{18}.\frac{5}{9}& \text{Uitwerken } \\ & =-bx-\frac{5}{9}b-\frac{1}{18}x-\frac{5}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{12}+b)(\frac{-9}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{9}{5}b+\frac{1}{3}b+\frac{1}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-9}{5})+\frac{1}{3})b+(\frac{-9}{15}) & \text{Neem samen} \\ &=-b^2-\frac{22}{15}b+(\frac{-9}{15}) & \text{Maak de som} \\ &=-b^2-\frac{22}{15}b+(\frac{-3}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{4}-q)(\frac{-15}{18}-p)& =(\color{red}{-q}+\color{orange}{\frac{13}{4}}).(\color{green}{-p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{13}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{6}q-\frac{13}{4}p-\frac{13}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =pq+\frac{5}{6}q-\frac{13}{4}p-\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{7}-b)(\frac{-3}{7}-b)& =(\color{red}{-b}+\color{orange}{\frac{-4}{7}}).(\color{green}{-b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{7}b+\frac{4}{7}b+\frac{4}{7}.\frac{3}{7}& \text{Uitwerken } \\ & =b^2+(\frac{3}{7}+\frac{4}{7})b+\frac{12}{49} & \text{Neem samen} \\ &=b^2+\frac{7}{7}b+\frac{12}{49} & \text{Maak de som} \\ &=b^2+1b+\frac{12}{49} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-10 19:23:58
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