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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{15}{20})(\frac{19}{15}-a)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{15}q+\frac{3}{4}a-\frac{3}{4}.\frac{19}{15}& \text{Uitwerken } \\ & =-aq+\frac{19}{15}q+\frac{3}{4}a-\frac{57}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{19}{15}q+\frac{3}{4}a-\frac{19}{20} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{10}{10})(a-\frac{12}{18})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}p+1a-1.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}p+1a-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{8}{16}-p)(a+\frac{-11}{14})& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{14}p+\frac{1}{2}a-\frac{1}{2}.\frac{11}{14}& \text{Uitwerken } \\ & =-ap+\frac{11}{14}p+\frac{1}{2}a-\frac{11}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{11}{19})(\frac{20}{17}+a)& =(\color{red}{x}+\color{orange}{\frac{-11}{19}}).(\color{green}{a}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{17}x-\frac{11}{19}a-\frac{11}{19}.\frac{20}{17}& \text{Uitwerken } \\ & =ax+\frac{20}{17}x-\frac{11}{19}a-\frac{220}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{12}{15})(\frac{-16}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p+\frac{4}{5}x-\frac{4}{5}.2& \text{Uitwerken } \\ & =px-2p+\frac{4}{5}x-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{14}-a)(q-\frac{10}{20})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}a+\frac{1}{2}q-\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}a+\frac{1}{2}q-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{6}-q)(p-\frac{-15}{6})& =(\color{red}{-q}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{2}q-\frac{8}{3}p-\frac{8}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq-\frac{5}{2}q-\frac{8}{3}p-\frac{40}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{2}q-\frac{8}{3}p-\frac{20}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-20}{2})(\frac{-12}{4}-q)& =(\color{red}{p}+\color{orange}{10}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(10)} . \color{green}{(-q)} + \color{orange}{(10)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -pq-3p-10q-10.3& \text{Uitwerken } \\ & =-pq-3p-10q-30 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{3}-p)(p+\frac{-6}{3})& =(\color{red}{-p}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp+2p+\frac{4}{3}p-\frac{4}{3}.2& \text{Uitwerken } \\ & =-p^2+(2+\frac{4}{3})p-\frac{8}{3} & \text{Neem samen} \\ &=-p^2+\frac{10}{3}p-\frac{8}{3} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-3}{19})(x-17)& =(\color{red}{b}+\color{orange}{\frac{-3}{19}}).(\color{green}{x}+\color{blue}{(-17)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-17)} + \color{orange}{(\frac{-3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = bx-17b-\frac{3}{19}x+\frac{3}{19}.17& \text{Uitwerken } \\ & =bx-17b-\frac{3}{19}x+\frac{51}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{19}{14})(q+\frac{4}{9})& =(\color{red}{x}+\color{orange}{\frac{-19}{14}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{9}x-\frac{19}{14}q-\frac{19}{14}.\frac{4}{9}& \text{Uitwerken } \\ & =qx+\frac{4}{9}x-\frac{19}{14}q-\frac{76}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{9}x-\frac{19}{14}q-\frac{38}{63} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{7}-x)(\frac{2}{13}+a)& =(\color{red}{-x}+\color{orange}{\frac{8}{7}}).(\color{green}{a}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{13}x+\frac{8}{7}a+\frac{8}{7}.\frac{2}{13}& \text{Uitwerken } \\ & =-ax-\frac{2}{13}x+\frac{8}{7}a+\frac{16}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-03 09:04:54