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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{1}{7})(\frac{-8}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{3}p+\frac{1}{7}q+\frac{1}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq-\frac{2}{3}p+\frac{1}{7}q+\frac{2}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-10}{8})(x-\frac{20}{12})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{3}x-\frac{5}{4}x+\frac{5}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{3})+(\frac{-5}{4}))x+\frac{25}{12} & \text{Neem samen} \\ &=x^2-\frac{35}{12}x+\frac{25}{12} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{2}-a)(x-\frac{-4}{19})& =(\color{red}{-a}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{19}a-4x-4.\frac{4}{19}& \text{Uitwerken } \\ & =-ax-\frac{4}{19}a-4x-\frac{16}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-7}{14})(x+\frac{20}{2})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = bx+10b-\frac{1}{2}x-\frac{1}{2}.10& \text{Uitwerken } \\ & =bx+10b-\frac{1}{2}x-\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+10b-\frac{1}{2}x-5 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{13}+q)(a-\frac{-4}{10})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{5}q+1a+1.\frac{2}{5}& \text{Uitwerken } \\ & =aq+\frac{2}{5}q+1a+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{3}{6})(\frac{8}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{9}a-\frac{1}{2}p-\frac{1}{2}.\frac{8}{9}& \text{Uitwerken } \\ & =ap+\frac{8}{9}a-\frac{1}{2}p-\frac{8}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{9}a-\frac{1}{2}p-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{1}{5})(\frac{-2}{15}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{5}}).(\color{green}{-x}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{15}q+\frac{1}{5}x+\frac{1}{5}.\frac{2}{15}& \text{Uitwerken } \\ & =-qx-\frac{2}{15}q+\frac{1}{5}x+\frac{2}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-(-11))(a-\frac{20}{3})& =(\color{red}{x}+\color{orange}{11}).(\color{green}{a}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(11)} . \color{green}{(a)} + \color{orange}{(11)} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{20}{3}x+11a-11.\frac{20}{3}& \text{Uitwerken } \\ & =ax-\frac{20}{3}x+11a-\frac{220}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{3}-q)(x+\frac{-1}{12})& =(\color{red}{-q}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{12}q+\frac{11}{3}x-\frac{11}{3}.\frac{1}{12}& \text{Uitwerken } \\ & =-qx+\frac{1}{12}q+\frac{11}{3}x-\frac{11}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-16}{13})(\frac{-1}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{16}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{16}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{9}q-\frac{16}{13}q-\frac{16}{13}.\frac{1}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{9})+(\frac{-16}{13}))q-\frac{16}{117} & \text{Neem samen} \\ &=-q^2-\frac{157}{117}q-\frac{16}{117} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-19}{12})(q+\frac{4}{8})& =(\color{red}{q}+\color{orange}{\frac{19}{12}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{19}{12})} . \color{green}{(q)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q+\frac{19}{12}q+\frac{19}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+\frac{19}{12})q+\frac{19}{24} & \text{Neem samen} \\ &=q^2+\frac{25}{12}q+\frac{19}{24} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-3}{15})(\frac{-2}{12}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{6}b-\frac{1}{5}p+\frac{1}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =bp-\frac{1}{6}b-\frac{1}{5}p+\frac{1}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-20 19:22:21
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