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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-17}{15})(p-\frac{-16}{20})& =(\color{red}{b}+\color{orange}{\frac{-17}{15}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}b-\frac{17}{15}p-\frac{17}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}b-\frac{17}{15}p-\frac{68}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-15}{3})(\frac{-19}{4}+q)& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{4}b-5q+5.\frac{19}{4}& \text{Uitwerken } \\ & =bq-\frac{19}{4}b-5q+\frac{95}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-3}{10})(\frac{14}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1q-\frac{3}{10}x+\frac{3}{10}.1& \text{Uitwerken } \\ & =-qx+1q-\frac{3}{10}x+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{4}{14})(\frac{-7}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{7}}).(\color{green}{p}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{15}b-\frac{2}{7}p+\frac{2}{7}.\frac{7}{15}& \text{Uitwerken } \\ & =bp-\frac{7}{15}b-\frac{2}{7}p+\frac{14}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{7}{15}b-\frac{2}{7}p+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{9}-b)(b+\frac{7}{8})& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{8}b+\frac{4}{3}b+\frac{4}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{8})+\frac{4}{3})b+(\frac{-28}{24}) & \text{Neem samen} \\ &=-b^2+\frac{11}{24}b+(\frac{-28}{24}) & \text{Maak de som} \\ &=-b^2+\frac{11}{24}b+(\frac{-7}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-11}{20})(p+\frac{-7}{9})& =(\color{red}{x}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{9}x-\frac{11}{20}p+\frac{11}{20}.\frac{7}{9}& \text{Uitwerken } \\ & =px-\frac{7}{9}x-\frac{11}{20}p+\frac{77}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{9}+q)(\frac{-9}{19}+a)& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{19}q+\frac{4}{3}a-\frac{4}{3}.\frac{9}{19}& \text{Uitwerken } \\ & =aq-\frac{9}{19}q+\frac{4}{3}a-\frac{36}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{9}{19}q+\frac{4}{3}a-\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{-12}{17})(\frac{-1}{16}+x)& =(\color{red}{q}+\color{orange}{\frac{12}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{12}{17})} . \color{green}{(x)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{16}q+\frac{12}{17}x-\frac{12}{17}.\frac{1}{16}& \text{Uitwerken } \\ & =qx-\frac{1}{16}q+\frac{12}{17}x-\frac{12}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{16}q+\frac{12}{17}x-\frac{3}{68} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-12}{3})(\frac{6}{8}-x)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{4}a-4x+4.\frac{3}{4}& \text{Uitwerken } \\ & =-ax+\frac{3}{4}a-4x+\frac{12}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{4}a-4x+3 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-5}{13}-x)(q+\frac{20}{13})& =(\color{red}{-x}+\color{orange}{\frac{-5}{13}}).(\color{green}{q}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{13}x-\frac{5}{13}q-\frac{5}{13}.\frac{20}{13}& \text{Uitwerken } \\ & =-qx-\frac{20}{13}x-\frac{5}{13}q-\frac{100}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{12}{12})(b+\frac{-1}{20})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{20}a+1b-1.\frac{1}{20}& \text{Uitwerken } \\ & =ab-\frac{1}{20}a+1b-\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-14}{13})(\frac{-1}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-14}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{16}q+\frac{14}{13}b+\frac{14}{13}.\frac{1}{16}& \text{Uitwerken } \\ & =-bq-\frac{1}{16}q+\frac{14}{13}b+\frac{14}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{16}q+\frac{14}{13}b+\frac{7}{104} & \text{Vereenvoudig} \\\end{align}\)
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