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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{20}-q)(a+\frac{16}{18})& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{8}{9}q+\frac{1}{5}a+\frac{1}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =-aq-\frac{8}{9}q+\frac{1}{5}a+\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-5}{17})(\frac{-11}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{-b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{5}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{11}{14}b-\frac{5}{17}b-\frac{5}{17}.\frac{11}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-11}{14})+(\frac{-5}{17}))b-\frac{55}{238} & \text{Neem samen} \\ &=-b^2-\frac{257}{238}b-\frac{55}{238} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{17}+a)(\frac{-11}{11}-b)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1a-1b-1.1& \text{Uitwerken } \\ & =-ab-1a-1b-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{10}{11}+p)(q+\frac{6}{12})& =(\color{red}{p}+\color{orange}{\frac{10}{11}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}p+\frac{10}{11}q+\frac{10}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}p+\frac{10}{11}q+\frac{10}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{2}p+\frac{10}{11}q+\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{10}-a)(\frac{-10}{7}+p)& =(\color{red}{-a}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{7}a+\frac{3}{5}p-\frac{3}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =-ap+\frac{10}{7}a+\frac{3}{5}p-\frac{30}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{10}{7}a+\frac{3}{5}p-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-18}{20})(b-\frac{-6}{19})& =(\color{red}{b}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{6}{19}b+\frac{9}{10}b+\frac{9}{10}.\frac{6}{19}& \text{Uitwerken } \\ & =b^2+(\frac{6}{19}+\frac{9}{10})b+\frac{54}{190} & \text{Neem samen} \\ &=b^2+\frac{231}{190}b+\frac{54}{190} & \text{Maak de som} \\ &=b^2+\frac{231}{190}b+\frac{27}{95} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-16}{17})(p-\frac{-4}{19})& =(\color{red}{q}+\color{orange}{\frac{-16}{17}}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{19}q-\frac{16}{17}p-\frac{16}{17}.\frac{4}{19}& \text{Uitwerken } \\ & =pq+\frac{4}{19}q-\frac{16}{17}p-\frac{64}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{10}+x)(\frac{15}{17}-x)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-x}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{15}{17}x+\frac{2}{5}x-\frac{2}{5}.\frac{15}{17}& \text{Uitwerken } \\ & =-x^2+(\frac{15}{17}+\frac{2}{5})x-\frac{30}{85} & \text{Neem samen} \\ &=-x^2+\frac{109}{85}x-\frac{30}{85} & \text{Maak de som} \\ &=-x^2+\frac{109}{85}x-\frac{6}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{7}+q)(q+\frac{12}{5})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{12}{5}q-\frac{6}{7}q-\frac{6}{7}.\frac{12}{5}& \text{Uitwerken } \\ & =q^2+(\frac{12}{5}+(\frac{-6}{7}))q-(\frac{-72}{35}) & \text{Neem samen} \\ &=q^2+\frac{54}{35}q-(\frac{-72}{35}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{7}+q)(\frac{13}{14}-q)& =(\color{red}{q}+\color{orange}{\frac{8}{7}}).(\color{green}{-q}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{13}{14}q-\frac{8}{7}q+\frac{8}{7}.\frac{13}{14}& \text{Uitwerken } \\ & =-q^2+(\frac{13}{14}+(\frac{-8}{7}))q+(\frac{-104}{98}) & \text{Neem samen} \\ &=-q^2-\frac{3}{14}q+(\frac{-104}{98}) & \text{Maak de som} \\ &=-q^2-\frac{3}{14}q+(\frac{-52}{49}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{17}{18}+q)(b+\frac{18}{19})& =(\color{red}{q}+\color{orange}{\frac{17}{18}}).(\color{green}{b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{19}q+\frac{17}{18}b+\frac{17}{18}.\frac{18}{19}& \text{Uitwerken } \\ & =bq+\frac{18}{19}q+\frac{17}{18}b+\frac{306}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{19}q+\frac{17}{18}b+\frac{17}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-19}{8})(p+8)& =(\color{red}{a}+\color{orange}{\frac{-19}{8}}).(\color{green}{p}+\color{blue}{8})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{-19}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ap+8a-\frac{19}{8}p-\frac{19}{8}.8& \text{Uitwerken } \\ & =ap+8a-\frac{19}{8}p-\frac{152}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+8a-\frac{19}{8}p-19 & \text{Vereenvoudig} \\\end{align}\)
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