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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-11}{19})(\frac{2}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{11}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}x-\frac{11}{19}q+\frac{11}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}x-\frac{11}{19}q+\frac{11}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{14}{4})(b-\frac{-4}{18})& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{9}a+\frac{7}{2}b+\frac{7}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =ab+\frac{2}{9}a+\frac{7}{2}b+\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{9}a+\frac{7}{2}b+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q-\frac{7}{18})(\frac{-20}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{-7}{18}}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{-7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qx-10q-\frac{7}{18}x+\frac{7}{18}.10& \text{Uitwerken } \\ & =qx-10q-\frac{7}{18}x+\frac{70}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-10q-\frac{7}{18}x+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{10}+x)(b-\frac{-7}{10})& =(\color{red}{x}+\color{orange}{\frac{-1}{10}}).(\color{green}{b}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{10}x-\frac{1}{10}b-\frac{1}{10}.\frac{7}{10}& \text{Uitwerken } \\ & =bx+\frac{7}{10}x-\frac{1}{10}b-\frac{7}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-13}{7})(\frac{-19}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{-13}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{18}p-\frac{13}{7}x+\frac{13}{7}.\frac{19}{18}& \text{Uitwerken } \\ & =px-\frac{19}{18}p-\frac{13}{7}x+\frac{247}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-14}{7})(q+\frac{-14}{5})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{5}x-2q+2.\frac{14}{5}& \text{Uitwerken } \\ & =qx-\frac{14}{5}x-2q+\frac{28}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{17}+x)(p-\frac{-9}{10})& =(\color{red}{x}+\color{orange}{\frac{-4}{17}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{10}x-\frac{4}{17}p-\frac{4}{17}.\frac{9}{10}& \text{Uitwerken } \\ & =px+\frac{9}{10}x-\frac{4}{17}p-\frac{36}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{10}x-\frac{4}{17}p-\frac{18}{85} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x+\frac{11}{20})(a-\frac{9}{10})& =(\color{red}{x}+\color{orange}{\frac{11}{20}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{10}x+\frac{11}{20}a-\frac{11}{20}.\frac{9}{10}& \text{Uitwerken } \\ & =ax-\frac{9}{10}x+\frac{11}{20}a-\frac{99}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{4}+p)(a-\frac{-15}{12})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{4}p-4a-4.\frac{5}{4}& \text{Uitwerken } \\ & =ap+\frac{5}{4}p-4a-\frac{20}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{4}p-4a-5 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{15}+b)(\frac{-5}{7}-b)& =(\color{red}{b}+\color{orange}{\frac{-11}{15}}).(\color{green}{-b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{7}b+\frac{11}{15}b+\frac{11}{15}.\frac{5}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{7})+\frac{11}{15})b+(\frac{-55}{105}) & \text{Neem samen} \\ &=-b^2+\frac{2}{105}b+(\frac{-55}{105}) & \text{Maak de som} \\ &=-b^2+\frac{2}{105}b+(\frac{-11}{21}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{10}+q)(x+\frac{-3}{19})& =(\color{red}{q}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{19}q+\frac{7}{5}x-\frac{7}{5}.\frac{3}{19}& \text{Uitwerken } \\ & =qx-\frac{3}{19}q+\frac{7}{5}x-\frac{21}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{9}+q)(q-\frac{-11}{2})& =(\color{red}{q}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{2}q-\frac{1}{9}q-\frac{1}{9}.\frac{11}{2}& \text{Uitwerken } \\ & =q^2+(\frac{11}{2}+(\frac{-1}{9}))q-(\frac{-11}{18}) & \text{Neem samen} \\ &=q^2+\frac{97}{18}q-(\frac{-11}{18}) & \text{Maak de som} \\\end{align}\)
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