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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{10}{18}-q)(b-\frac{-7}{18})& =(\color{red}{-q}+\color{orange}{\frac{5}{9}}).(\color{green}{b}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{18}q+\frac{5}{9}b+\frac{5}{9}.\frac{7}{18}& \text{Uitwerken } \\ & =-bq-\frac{7}{18}q+\frac{5}{9}b+\frac{35}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-18}{8})(b-\frac{-4}{8})& =(\color{red}{p}+\color{orange}{\frac{-9}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}p-\frac{9}{4}b-\frac{9}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}p-\frac{9}{4}b-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-17}{15})(b+\frac{18}{19})& =(\color{red}{q}+\color{orange}{\frac{17}{15}}).(\color{green}{b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{17}{15})} . \color{green}{(b)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{19}q+\frac{17}{15}b+\frac{17}{15}.\frac{18}{19}& \text{Uitwerken } \\ & =bq+\frac{18}{19}q+\frac{17}{15}b+\frac{306}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{19}q+\frac{17}{15}b+\frac{102}{95} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{10}-x)(x-\frac{1}{14})& =(\color{red}{-x}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{14}x-\frac{4}{5}x+\frac{4}{5}.\frac{1}{14}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{14}+(\frac{-4}{5}))x+(\frac{-4}{70}) & \text{Neem samen} \\ &=-x^2-\frac{51}{70}x+(\frac{-4}{70}) & \text{Maak de som} \\ &=-x^2-\frac{51}{70}x+(\frac{-2}{35}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{5}-p)(p+\frac{-20}{5})& =(\color{red}{-p}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-4)} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -pp+4p+\frac{7}{5}p-\frac{7}{5}.4& \text{Uitwerken } \\ & =-p^2+(4+\frac{7}{5})p-\frac{28}{5} & \text{Neem samen} \\ &=-p^2+\frac{27}{5}p-\frac{28}{5} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-18}{6})(a+\frac{-12}{18})& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}p-3a+3.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}p-3a+\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{3}p-3a+2 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{9}+a)(\frac{-18}{20}-x)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{10}a+1x+1.\frac{9}{10}& \text{Uitwerken } \\ & =-ax-\frac{9}{10}a+1x+\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(9-q)(q+\frac{7}{8})& =(\color{red}{-q}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{7}{8}q+9q+9.\frac{7}{8}& \text{Uitwerken } \\ & =-q^2+((\frac{-7}{8})+9)q+(\frac{-63}{8}) & \text{Neem samen} \\ &=-q^2+\frac{65}{8}q+(\frac{-63}{8}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(x-\frac{10}{8})(\frac{14}{3}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{-b}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{14}{3}x+\frac{5}{4}b-\frac{5}{4}.\frac{14}{3}& \text{Uitwerken } \\ & =-bx+\frac{14}{3}x+\frac{5}{4}b-\frac{70}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{14}{3}x+\frac{5}{4}b-\frac{35}{6} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-18}{11})(x-\frac{-11}{17})& =(\color{red}{b}+\color{orange}{\frac{18}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{18}{11})} . \color{green}{(x)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{17}b+\frac{18}{11}x+\frac{18}{11}.\frac{11}{17}& \text{Uitwerken } \\ & =bx+\frac{11}{17}b+\frac{18}{11}x+\frac{198}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{17}b+\frac{18}{11}x+\frac{18}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{11}-x)(x-\frac{-20}{2})& =(\color{red}{-x}+\color{orange}{\frac{16}{11}}).(\color{green}{x}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(10)} + \color{orange}{(\frac{16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -xx-10x+\frac{16}{11}x+\frac{16}{11}.10& \text{Uitwerken } \\ & =-x^2+((-10)+\frac{16}{11})x+(\frac{-160}{11}) & \text{Neem samen} \\ &=-x^2-\frac{94}{11}x+(\frac{-160}{11}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b-\frac{14}{9})(x-\frac{-13}{20})& =(\color{red}{b}+\color{orange}{\frac{-14}{9}}).(\color{green}{x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{20}b-\frac{14}{9}x-\frac{14}{9}.\frac{13}{20}& \text{Uitwerken } \\ & =bx+\frac{13}{20}b-\frac{14}{9}x-\frac{182}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{13}{20}b-\frac{14}{9}x-\frac{91}{90} & \text{Vereenvoudig} \\\end{align}\)
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