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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-9}{20})(\frac{-12}{2}+a)& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{-9}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = aq-6q-\frac{9}{20}a+\frac{9}{20}.6& \text{Uitwerken } \\ & =aq-6q-\frac{9}{20}a+\frac{54}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-6q-\frac{9}{20}a+\frac{27}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-8}{7})(a-\frac{20}{4})& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ab-5b-\frac{8}{7}a+\frac{8}{7}.5& \text{Uitwerken } \\ & =ab-5b-\frac{8}{7}a+\frac{40}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{2}+a)(x-\frac{20}{20})& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{5}{2}x-\frac{5}{2}.1& \text{Uitwerken } \\ & =ax-1a+\frac{5}{2}x-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{3}{19}-q)(\frac{9}{19}+a)& =(\color{red}{-q}+\color{orange}{\frac{3}{19}}).(\color{green}{a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{3}{19})} . \color{green}{(a)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{19}q+\frac{3}{19}a+\frac{3}{19}.\frac{9}{19}& \text{Uitwerken } \\ & =-aq-\frac{9}{19}q+\frac{3}{19}a+\frac{27}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}((-12)-a)(\frac{12}{7}-q)& =(\color{red}{-a}+\color{orange}{(-12)}).(\color{green}{-q}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(-12)} . \color{green}{(-q)} + \color{orange}{(-12)} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{7}a+12q-12.\frac{12}{7}& \text{Uitwerken } \\ & =aq-\frac{12}{7}a+12q-\frac{144}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-9}{11})(a-\frac{-12}{16})& =(\color{red}{a}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{4}a-\frac{9}{11}a-\frac{9}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+(\frac{3}{4}+(\frac{-9}{11}))a-(\frac{-27}{44}) & \text{Neem samen} \\ &=a^2-\frac{3}{44}a-(\frac{-27}{44}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-13}{9})(\frac{-7}{17}+b)& =(\color{red}{q}+\color{orange}{\frac{-13}{9}}).(\color{green}{b}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{17}q-\frac{13}{9}b+\frac{13}{9}.\frac{7}{17}& \text{Uitwerken } \\ & =bq-\frac{7}{17}q-\frac{13}{9}b+\frac{91}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{6}{20})(\frac{13}{15}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{-a}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{15}p-\frac{3}{10}a+\frac{3}{10}.\frac{13}{15}& \text{Uitwerken } \\ & =-ap+\frac{13}{15}p-\frac{3}{10}a+\frac{39}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{13}{15}p-\frac{3}{10}a+\frac{13}{50} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{2}-q)(b+\frac{3}{20})& =(\color{red}{-q}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{20}q-5b-5.\frac{3}{20}& \text{Uitwerken } \\ & =-bq-\frac{3}{20}q-5b-\frac{15}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{3}{20}q-5b-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{12}-x)(q+\frac{-2}{18})& =(\color{red}{-x}+\color{orange}{\frac{17}{12}}).(\color{green}{q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{9}x+\frac{17}{12}q-\frac{17}{12}.\frac{1}{9}& \text{Uitwerken } \\ & =-qx+\frac{1}{9}x+\frac{17}{12}q-\frac{17}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-6}{9}+b)(\frac{-20}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bp-5b-\frac{2}{3}p+\frac{2}{3}.5& \text{Uitwerken } \\ & =bp-5b-\frac{2}{3}p+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-17}{20})(\frac{15}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{17}{20}}).(\color{green}{-b}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{17}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{15}{16}q-\frac{17}{20}b+\frac{17}{20}.\frac{15}{16}& \text{Uitwerken } \\ & =-bq+\frac{15}{16}q-\frac{17}{20}b+\frac{255}{320} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{15}{16}q-\frac{17}{20}b+\frac{51}{64} & \text{Vereenvoudig} \\\end{align}\)
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