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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}((-9)-a)(q+\frac{17}{18})& =(\color{red}{-a}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{18}a-9q-9.\frac{17}{18}& \text{Uitwerken } \\ & =-aq-\frac{17}{18}a-9q-\frac{153}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{17}{18}a-9q-\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{5}+q)(\frac{18}{18}-q)& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qq+1q-\frac{2}{5}q+\frac{2}{5}.1& \text{Uitwerken } \\ & =-q^2+(1+(\frac{-2}{5}))q+(\frac{-2}{5}) & \text{Neem samen} \\ &=-q^2+\frac{3}{5}q+(\frac{-2}{5}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-19}{17})(\frac{-4}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{19}{17}}).(\color{green}{-p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{19}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{9}b-\frac{19}{17}p-\frac{19}{17}.\frac{2}{9}& \text{Uitwerken } \\ & =-bp-\frac{2}{9}b-\frac{19}{17}p-\frac{38}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{2}+b)((-20)+q)& =(\color{red}{b}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-20)} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = bq-20b+\frac{9}{2}q-\frac{9}{2}.20& \text{Uitwerken } \\ & =bq-20b+\frac{9}{2}q-\frac{180}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-20b+\frac{9}{2}q-90 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-13}{18}-a)(a+\frac{4}{15})& =(\color{red}{-a}+\color{orange}{\frac{-13}{18}}).(\color{green}{a}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{4}{15}a-\frac{13}{18}a-\frac{13}{18}.\frac{4}{15}& \text{Uitwerken } \\ & =-a^2+((\frac{-4}{15})+(\frac{-13}{18}))a-\frac{52}{270} & \text{Neem samen} \\ &=-a^2-\frac{89}{90}a-\frac{52}{270} & \text{Maak de som} \\ &=-a^2-\frac{89}{90}a-\frac{26}{135} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-14}{17})(\frac{-17}{7}+a)& =(\color{red}{q}+\color{orange}{\frac{14}{17}}).(\color{green}{a}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{14}{17})} . \color{green}{(a)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{7}q+\frac{14}{17}a-\frac{14}{17}.\frac{17}{7}& \text{Uitwerken } \\ & =aq-\frac{17}{7}q+\frac{14}{17}a-\frac{238}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{7}q+\frac{14}{17}a-2 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{17}{19})(p-\frac{13}{7})& =(\color{red}{b}+\color{orange}{\frac{17}{19}}).(\color{green}{p}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{7}b+\frac{17}{19}p-\frac{17}{19}.\frac{13}{7}& \text{Uitwerken } \\ & =bp-\frac{13}{7}b+\frac{17}{19}p-\frac{221}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-2}{13})(q+\frac{-5}{14})& =(\color{red}{p}+\color{orange}{\frac{2}{13}}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{2}{13})} . \color{green}{(q)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{14}p+\frac{2}{13}q-\frac{2}{13}.\frac{5}{14}& \text{Uitwerken } \\ & =pq-\frac{5}{14}p+\frac{2}{13}q-\frac{10}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{14}p+\frac{2}{13}q-\frac{5}{91} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{8}-b)(p+\frac{-11}{19})& =(\color{red}{-b}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{19}b+\frac{5}{2}p-\frac{5}{2}.\frac{11}{19}& \text{Uitwerken } \\ & =-bp+\frac{11}{19}b+\frac{5}{2}p-\frac{55}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-2}{11})(x+\frac{-8}{7})& =(\color{red}{x}+\color{orange}{\frac{-2}{11}}).(\color{green}{x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{7}x-\frac{2}{11}x+\frac{2}{11}.\frac{8}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{7})+(\frac{-2}{11}))x+\frac{16}{77} & \text{Neem samen} \\ &=x^2-\frac{102}{77}x+\frac{16}{77} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-11}{9})(q+\frac{-15}{13})& =(\color{red}{q}+\color{orange}{\frac{11}{9}}).(\color{green}{q}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{13}q+\frac{11}{9}q-\frac{11}{9}.\frac{15}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{13})+\frac{11}{9})q-(\frac{-165}{117}) & \text{Neem samen} \\ &=q^2+\frac{8}{117}q-(\frac{-165}{117}) & \text{Maak de som} \\ &=q^2+\frac{8}{117}q+\frac{55}{39} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{8}-p)(a+\frac{-8}{13})& =(\color{red}{-p}+\color{orange}{\frac{15}{8}}).(\color{green}{a}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{13}p+\frac{15}{8}a-\frac{15}{8}.\frac{8}{13}& \text{Uitwerken } \\ & =-ap+\frac{8}{13}p+\frac{15}{8}a-\frac{120}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{8}{13}p+\frac{15}{8}a-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
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