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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-19}{10})(\frac{9}{5}-b)& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{-b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{5}p-\frac{19}{10}b+\frac{19}{10}.\frac{9}{5}& \text{Uitwerken } \\ & =-bp+\frac{9}{5}p-\frac{19}{10}b+\frac{171}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{12}-p)(\frac{-11}{17}+a)& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{17}p+\frac{2}{3}a-\frac{2}{3}.\frac{11}{17}& \text{Uitwerken } \\ & =-ap+\frac{11}{17}p+\frac{2}{3}a-\frac{22}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{6}+b)(\frac{-1}{16}-q)& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{-q}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{16}b-\frac{7}{6}q-\frac{7}{6}.\frac{1}{16}& \text{Uitwerken } \\ & =-bq-\frac{1}{16}b-\frac{7}{6}q-\frac{7}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{15}-x)(\frac{-6}{17}+a)& =(\color{red}{-x}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{6}{17}x-\frac{2}{5}a+\frac{2}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =-ax+\frac{6}{17}x-\frac{2}{5}a+\frac{12}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{12}+q)(\frac{6}{20}+b)& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{10}q-\frac{1}{4}b-\frac{1}{4}.\frac{3}{10}& \text{Uitwerken } \\ & =bq+\frac{3}{10}q-\frac{1}{4}b-\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{12}-b)(x+\frac{7}{5})& =(\color{red}{-b}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{7}{5}b+\frac{1}{2}x+\frac{1}{2}.\frac{7}{5}& \text{Uitwerken } \\ & =-bx-\frac{7}{5}b+\frac{1}{2}x+\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-16}{5})(\frac{13}{12}+p)& =(\color{red}{a}+\color{orange}{\frac{16}{5}}).(\color{green}{p}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{16}{5})} . \color{green}{(p)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{12}a+\frac{16}{5}p+\frac{16}{5}.\frac{13}{12}& \text{Uitwerken } \\ & =ap+\frac{13}{12}a+\frac{16}{5}p+\frac{208}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{13}{12}a+\frac{16}{5}p+\frac{52}{15} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p+\frac{12}{20})(p+\frac{19}{5})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{5}p+\frac{3}{5}p+\frac{3}{5}.\frac{19}{5}& \text{Uitwerken } \\ & =p^2+(\frac{19}{5}+\frac{3}{5})p+\frac{57}{25} & \text{Neem samen} \\ &=p^2+\frac{22}{5}p+\frac{57}{25} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(q-\frac{3}{4})(\frac{-1}{11}-p)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{11}q+\frac{3}{4}p+\frac{3}{4}.\frac{1}{11}& \text{Uitwerken } \\ & =-pq-\frac{1}{11}q+\frac{3}{4}p+\frac{3}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-5}{6})(\frac{-9}{11}+a)& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{a}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{11}p+\frac{5}{6}a-\frac{5}{6}.\frac{9}{11}& \text{Uitwerken } \\ & =ap-\frac{9}{11}p+\frac{5}{6}a-\frac{45}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{11}p+\frac{5}{6}a-\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{3}{18})(q+\frac{16}{3})& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{q}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{3}p-\frac{1}{6}q-\frac{1}{6}.\frac{16}{3}& \text{Uitwerken } \\ & =pq+\frac{16}{3}p-\frac{1}{6}q-\frac{16}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{16}{3}p-\frac{1}{6}q-\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{9}{11})(b-\frac{2}{18})& =(\color{red}{x}+\color{orange}{\frac{-9}{11}}).(\color{green}{b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{9}x-\frac{9}{11}b+\frac{9}{11}.\frac{1}{9}& \text{Uitwerken } \\ & =bx-\frac{1}{9}x-\frac{9}{11}b+\frac{9}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{9}x-\frac{9}{11}b+\frac{1}{11} & \text{Vereenvoudig} \\\end{align}\)
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