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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{10}{20})(b-\frac{-17}{3})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{3}q+\frac{1}{2}b+\frac{1}{2}.\frac{17}{3}& \text{Uitwerken } \\ & =bq+\frac{17}{3}q+\frac{1}{2}b+\frac{17}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{8}{7})(p+\frac{-6}{8})& =(\color{red}{p}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{4}p+\frac{8}{7}p-\frac{8}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{4})+\frac{8}{7})p-(\frac{-24}{28}) & \text{Neem samen} \\ &=p^2+\frac{11}{28}p-(\frac{-24}{28}) & \text{Maak de som} \\ &=p^2+\frac{11}{28}p+\frac{6}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{2}-b)(a+\frac{-2}{16})& =(\color{red}{-b}+\color{orange}{9}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(9)} . \color{green}{(a)} + \color{orange}{(9)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{8}b+9a-9.\frac{1}{8}& \text{Uitwerken } \\ & =-ab+\frac{1}{8}b+9a-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{13}{4})(a+\frac{-8}{17})& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{a}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{17}b-\frac{13}{4}a+\frac{13}{4}.\frac{8}{17}& \text{Uitwerken } \\ & =ab-\frac{8}{17}b-\frac{13}{4}a+\frac{104}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{8}{17}b-\frac{13}{4}a+\frac{26}{17} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{10}-q)(\frac{-4}{16}+b)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{4}q+\frac{1}{2}b-\frac{1}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-bq+\frac{1}{4}q+\frac{1}{2}b-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+1)(\frac{-19}{9}+q)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{9}a+1q-1.\frac{19}{9}& \text{Uitwerken } \\ & =aq-\frac{19}{9}a+1q-\frac{19}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{12}{8})(q-\frac{15}{15})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b-\frac{3}{2}q+\frac{3}{2}.1& \text{Uitwerken } \\ & =bq-1b-\frac{3}{2}q+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-11}{13}-x)(\frac{-12}{9}-a)& =(\color{red}{-x}+\color{orange}{\frac{-11}{13}}).(\color{green}{-a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{3}x+\frac{11}{13}a+\frac{11}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =ax+\frac{4}{3}x+\frac{11}{13}a+\frac{44}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-7}{15})(x+\frac{-18}{20})& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{10}b-\frac{7}{15}x+\frac{7}{15}.\frac{9}{10}& \text{Uitwerken } \\ & =bx-\frac{9}{10}b-\frac{7}{15}x+\frac{63}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{9}{10}b-\frac{7}{15}x+\frac{21}{50} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{7}+a)(\frac{9}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{7}}).(\color{green}{b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{19}{7})} . \color{green}{(b)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{17}a+\frac{19}{7}b+\frac{19}{7}.\frac{9}{17}& \text{Uitwerken } \\ & =ab+\frac{9}{17}a+\frac{19}{7}b+\frac{171}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-4}{20})(b-9)& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-9)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bx-9x-\frac{1}{5}b+\frac{1}{5}.9& \text{Uitwerken } \\ & =bx-9x-\frac{1}{5}b+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{3}+x)(a+\frac{-17}{20})& =(\color{red}{x}+\color{orange}{\frac{-19}{3}}).(\color{green}{a}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{20}x-\frac{19}{3}a+\frac{19}{3}.\frac{17}{20}& \text{Uitwerken } \\ & =ax-\frac{17}{20}x-\frac{19}{3}a+\frac{323}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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