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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{14}{20}+a)(x+\frac{18}{17})& =(\color{red}{a}+\color{orange}{\frac{7}{10}}).(\color{green}{x}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{17}a+\frac{7}{10}x+\frac{7}{10}.\frac{18}{17}& \text{Uitwerken } \\ & =ax+\frac{18}{17}a+\frac{7}{10}x+\frac{126}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{17}a+\frac{7}{10}x+\frac{63}{85} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{5}-q)(\frac{-13}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{-12}{5}}).(\color{green}{-b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{9}q+\frac{12}{5}b+\frac{12}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =bq+\frac{13}{9}q+\frac{12}{5}b+\frac{156}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{13}{9}q+\frac{12}{5}b+\frac{52}{15} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-10}{16})(\frac{19}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{8}}).(\color{green}{a}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{12}b+\frac{5}{8}a+\frac{5}{8}.\frac{19}{12}& \text{Uitwerken } \\ & =ab+\frac{19}{12}b+\frac{5}{8}a+\frac{95}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{6}{18})(p-\frac{-4}{19})& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{19}a+\frac{1}{3}p+\frac{1}{3}.\frac{4}{19}& \text{Uitwerken } \\ & =ap+\frac{4}{19}a+\frac{1}{3}p+\frac{4}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{10}-q)(\frac{-14}{15}+a)& =(\color{red}{-q}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{14}{15}q-\frac{1}{5}a+\frac{1}{5}.\frac{14}{15}& \text{Uitwerken } \\ & =-aq+\frac{14}{15}q-\frac{1}{5}a+\frac{14}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{6}-x)(a+\frac{11}{2})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{2}x+1a+1.\frac{11}{2}& \text{Uitwerken } \\ & =-ax-\frac{11}{2}x+1a+\frac{11}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{20}{9})(\frac{8}{11}+a)& =(\color{red}{p}+\color{orange}{\frac{20}{9}}).(\color{green}{a}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{20}{9})} . \color{green}{(a)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{11}p+\frac{20}{9}a+\frac{20}{9}.\frac{8}{11}& \text{Uitwerken } \\ & =ap+\frac{8}{11}p+\frac{20}{9}a+\frac{160}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-9}{5})(\frac{16}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{9}{5}}).(\color{green}{b}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ab+8a+\frac{9}{5}b+\frac{9}{5}.8& \text{Uitwerken } \\ & =ab+8a+\frac{9}{5}b+\frac{72}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{2}-x)(18+a)& =(\color{red}{-x}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{18})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(18)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -ax-18x-\frac{5}{2}a-\frac{5}{2}.18& \text{Uitwerken } \\ & =-ax-18x-\frac{5}{2}a-\frac{90}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-18x-\frac{5}{2}a-45 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{1}{16})(\frac{-12}{14}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{16}}).(\color{green}{-p}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{7}p+\frac{1}{16}p+\frac{1}{16}.\frac{6}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{7})+\frac{1}{16})p+(\frac{-6}{112}) & \text{Neem samen} \\ &=-p^2-\frac{89}{112}p+(\frac{-6}{112}) & \text{Maak de som} \\ &=-p^2-\frac{89}{112}p+(\frac{-3}{56}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{19}+x)(x+9)& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(9)} + \color{orange}{(\frac{10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = xx+9x+\frac{10}{19}x+\frac{10}{19}.9& \text{Uitwerken } \\ & =x^2+(9+\frac{10}{19})x+\frac{90}{19} & \text{Neem samen} \\ &=x^2+\frac{181}{19}x+\frac{90}{19} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}((-18)+a)(a-\frac{15}{17})& =(\color{red}{a}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{15}{17}a-18a+18.\frac{15}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-15}{17})+(-18))a+\frac{270}{17} & \text{Neem samen} \\ &=a^2-\frac{321}{17}a+\frac{270}{17} & \text{Maak de som} \\\end{align}\)
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