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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-5}{19})(\frac{-5}{12}-x)& =(\color{red}{q}+\color{orange}{\frac{-5}{19}}).(\color{green}{-x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{12}q+\frac{5}{19}x+\frac{5}{19}.\frac{5}{12}& \text{Uitwerken } \\ & =-qx-\frac{5}{12}q+\frac{5}{19}x+\frac{25}{228} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-2}{20})(\frac{5}{16}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{-x}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{16}q+\frac{1}{10}x-\frac{1}{10}.\frac{5}{16}& \text{Uitwerken } \\ & =-qx+\frac{5}{16}q+\frac{1}{10}x-\frac{5}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{5}{16}q+\frac{1}{10}x-\frac{1}{32} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{6}+p)(x-\frac{5}{5})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+3x-3.1& \text{Uitwerken } \\ & =px-1p+3x-3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{10}-x)(\frac{14}{10}-p)& =(\color{red}{-x}+\color{orange}{\frac{6}{5}}).(\color{green}{-p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{5}x-\frac{6}{5}p+\frac{6}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =px-\frac{7}{5}x-\frac{6}{5}p+\frac{42}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{15}-x)(q-\frac{-15}{11})& =(\color{red}{-x}+\color{orange}{\frac{-4}{15}}).(\color{green}{q}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{11}x-\frac{4}{15}q-\frac{4}{15}.\frac{15}{11}& \text{Uitwerken } \\ & =-qx-\frac{15}{11}x-\frac{4}{15}q-\frac{60}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{15}{11}x-\frac{4}{15}q-\frac{4}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{17}-q)(\frac{13}{9}+x)& =(\color{red}{-q}+\color{orange}{\frac{-16}{17}}).(\color{green}{x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{9}q-\frac{16}{17}x-\frac{16}{17}.\frac{13}{9}& \text{Uitwerken } \\ & =-qx-\frac{13}{9}q-\frac{16}{17}x-\frac{208}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{8}{3})(\frac{17}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{-8}{3}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-\frac{8}{3}b-\frac{8}{3}.1& \text{Uitwerken } \\ & =bx+1x-\frac{8}{3}b-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-17}{11})(\frac{19}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-17}{11}}).(\color{green}{b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{2}a-\frac{17}{11}b-\frac{17}{11}.\frac{19}{2}& \text{Uitwerken } \\ & =ab+\frac{19}{2}a-\frac{17}{11}b-\frac{323}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{18}{3})(a-\frac{15}{2})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{2}x+6a-6.\frac{15}{2}& \text{Uitwerken } \\ & =ax-\frac{15}{2}x+6a-\frac{90}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{15}{2}x+6a-45 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{19}{10})(p-\frac{-1}{4})& =(\color{red}{p}+\color{orange}{\frac{-19}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{4}p-\frac{19}{10}p-\frac{19}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =p^2+(\frac{1}{4}+(\frac{-19}{10}))p-(\frac{-19}{40}) & \text{Neem samen} \\ &=p^2-\frac{33}{20}p-(\frac{-19}{40}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{17}+q)(b-\frac{-11}{8})& =(\color{red}{q}+\color{orange}{\frac{10}{17}}).(\color{green}{b}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{10}{17})} . \color{green}{(b)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{8}q+\frac{10}{17}b+\frac{10}{17}.\frac{11}{8}& \text{Uitwerken } \\ & =bq+\frac{11}{8}q+\frac{10}{17}b+\frac{110}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{11}{8}q+\frac{10}{17}b+\frac{55}{68} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{6}{11})(\frac{16}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{-p}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{16}{15}b+\frac{6}{11}p-\frac{6}{11}.\frac{16}{15}& \text{Uitwerken } \\ & =-bp+\frac{16}{15}b+\frac{6}{11}p-\frac{96}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{16}{15}b+\frac{6}{11}p-\frac{32}{55} & \text{Vereenvoudig} \\\end{align}\)
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