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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{14}+a)(b-\frac{19}{11})& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{11}a-\frac{3}{7}b+\frac{3}{7}.\frac{19}{11}& \text{Uitwerken } \\ & =ab-\frac{19}{11}a-\frac{3}{7}b+\frac{57}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-10}{8}+x)(a-\frac{-16}{5})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{5}x-\frac{5}{4}a-\frac{5}{4}.\frac{16}{5}& \text{Uitwerken } \\ & =ax+\frac{16}{5}x-\frac{5}{4}a-\frac{80}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{16}{5}x-\frac{5}{4}a-4 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-1}{7})(\frac{18}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{1}{7}}).(\color{green}{-q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{18}{5}p-\frac{1}{7}q+\frac{1}{7}.\frac{18}{5}& \text{Uitwerken } \\ & =-pq+\frac{18}{5}p-\frac{1}{7}q+\frac{18}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-20}{15})(\frac{16}{18}-p)& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{9}a+\frac{4}{3}p-\frac{4}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =-ap+\frac{8}{9}a+\frac{4}{3}p-\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{7}+x)(\frac{-10}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{-18}{7}}).(\color{green}{-a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{7}x+\frac{18}{7}a+\frac{18}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =-ax-\frac{5}{7}x+\frac{18}{7}a+\frac{90}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{11}{8})(\frac{3}{8}+b)& =(\color{red}{q}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{8}q+\frac{11}{8}b+\frac{11}{8}.\frac{3}{8}& \text{Uitwerken } \\ & =bq+\frac{3}{8}q+\frac{11}{8}b+\frac{33}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{6}+a)(x-\frac{-15}{18})& =(\color{red}{a}+\color{orange}{\frac{11}{6}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{11}{6})} . \color{green}{(x)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{6}a+\frac{11}{6}x+\frac{11}{6}.\frac{5}{6}& \text{Uitwerken } \\ & =ax+\frac{5}{6}a+\frac{11}{6}x+\frac{55}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-13}{6})(a+\frac{2}{12})& =(\color{red}{x}+\color{orange}{\frac{-13}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{6}x-\frac{13}{6}a-\frac{13}{6}.\frac{1}{6}& \text{Uitwerken } \\ & =ax+\frac{1}{6}x-\frac{13}{6}a-\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-1}{12})(a+\frac{18}{8})& =(\color{red}{x}+\color{orange}{\frac{1}{12}}).(\color{green}{a}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{1}{12})} . \color{green}{(a)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{4}x+\frac{1}{12}a+\frac{1}{12}.\frac{9}{4}& \text{Uitwerken } \\ & =ax+\frac{9}{4}x+\frac{1}{12}a+\frac{9}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{4}x+\frac{1}{12}a+\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(4+q)(q-\frac{-3}{3})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq+1q+4q+4.1& \text{Uitwerken } \\ & =q^2+(1+4)q+4 & \text{Neem samen} \\ &=q^2+5q+4 & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{5}{5})(x+\frac{19}{19})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a-1x-1.1& \text{Uitwerken } \\ & =ax+1a-1x-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-14}{17})(\frac{12}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{14}{17}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{14}{17})} . \color{green}{(a)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}x+\frac{14}{17}a+\frac{14}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}x+\frac{14}{17}a+\frac{42}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{4}x+\frac{14}{17}a+\frac{21}{34} & \text{Vereenvoudig} \\\end{align}\)
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