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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-19}{11})(b+\frac{13}{15})& =(\color{red}{x}+\color{orange}{\frac{-19}{11}}).(\color{green}{b}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{15}x-\frac{19}{11}b-\frac{19}{11}.\frac{13}{15}& \text{Uitwerken } \\ & =bx+\frac{13}{15}x-\frac{19}{11}b-\frac{247}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{3}-x)(p+\frac{-8}{11})& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{8}{11}x-\frac{1}{3}p+\frac{1}{3}.\frac{8}{11}& \text{Uitwerken } \\ & =-px+\frac{8}{11}x-\frac{1}{3}p+\frac{8}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{16}-x)(p-\frac{14}{5})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{14}{5}x-1p+1.\frac{14}{5}& \text{Uitwerken } \\ & =-px+\frac{14}{5}x-1p+\frac{14}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-7}{6})(\frac{19}{16}-a)& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{-a}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{16}q+\frac{7}{6}a-\frac{7}{6}.\frac{19}{16}& \text{Uitwerken } \\ & =-aq+\frac{19}{16}q+\frac{7}{6}a-\frac{133}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+18)(\frac{-15}{9}+a)& =(\color{red}{x}+\color{orange}{18}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(18)} . \color{green}{(a)} + \color{orange}{(18)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}x+18a-18.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}x+18a-\frac{90}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{3}x+18a-30 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-4}{7})(\frac{-1}{15}+x)& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{x}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{15}p+\frac{4}{7}x-\frac{4}{7}.\frac{1}{15}& \text{Uitwerken } \\ & =px-\frac{1}{15}p+\frac{4}{7}x-\frac{4}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{4}+b)(q-\frac{-1}{3})& =(\color{red}{b}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}b+5q+5.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}b+5q+\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{10}-q)(a+7)& =(\color{red}{-q}+\color{orange}{\frac{-17}{10}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(7)} + \color{orange}{(\frac{-17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -aq-7q-\frac{17}{10}a-\frac{17}{10}.7& \text{Uitwerken } \\ & =-aq-7q-\frac{17}{10}a-\frac{119}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-10}{16})(\frac{-10}{12}-q)& =(\color{red}{a}+\color{orange}{\frac{-5}{8}}).(\color{green}{-q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{6}a+\frac{5}{8}q+\frac{5}{8}.\frac{5}{6}& \text{Uitwerken } \\ & =-aq-\frac{5}{6}a+\frac{5}{8}q+\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-6}{3})(p-\frac{4}{11})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{11}x-2p+2.\frac{4}{11}& \text{Uitwerken } \\ & =px-\frac{4}{11}x-2p+\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{14}{11})(b+\frac{9}{12})& =(\color{red}{a}+\color{orange}{\frac{-14}{11}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}a-\frac{14}{11}b-\frac{14}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}a-\frac{14}{11}b-\frac{42}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{4}a-\frac{14}{11}b-\frac{21}{22} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-14}{5})(a+\frac{10}{4})& =(\color{red}{a}+\color{orange}{\frac{14}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{2}a+\frac{14}{5}a+\frac{14}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+(\frac{5}{2}+\frac{14}{5})a+\frac{70}{10} & \text{Neem samen} \\ &=a^2+\frac{53}{10}a+\frac{70}{10} & \text{Maak de som} \\ &=a^2+\frac{53}{10}a+7 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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