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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{3}-p)(a+\frac{-16}{6})& =(\color{red}{-p}+\color{orange}{\frac{-16}{3}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{3}p-\frac{16}{3}a+\frac{16}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =-ap+\frac{8}{3}p-\frac{16}{3}a+\frac{128}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{13}+p)(p-\frac{16}{6})& =(\color{red}{p}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{3}p+\frac{18}{13}p-\frac{18}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{3})+\frac{18}{13})p-(\frac{-144}{39}) & \text{Neem samen} \\ &=p^2-\frac{50}{39}p-(\frac{-144}{39}) & \text{Maak de som} \\ &=p^2-\frac{50}{39}p+\frac{48}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{13}-b)(\frac{11}{16}+a)& =(\color{red}{-b}+\color{orange}{\frac{14}{13}}).(\color{green}{a}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{14}{13})} . \color{green}{(a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{16}b+\frac{14}{13}a+\frac{14}{13}.\frac{11}{16}& \text{Uitwerken } \\ & =-ab-\frac{11}{16}b+\frac{14}{13}a+\frac{154}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{11}{16}b+\frac{14}{13}a+\frac{77}{104} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-4}{11})(\frac{12}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{-4}{11}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{2}a+\frac{4}{11}b-\frac{4}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =-ab+\frac{3}{2}a+\frac{4}{11}b-\frac{12}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{3}{2}a+\frac{4}{11}b-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{20}-a)(x+\frac{1}{8})& =(\color{red}{-a}+\color{orange}{\frac{-7}{10}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{8}a-\frac{7}{10}x-\frac{7}{10}.\frac{1}{8}& \text{Uitwerken } \\ & =-ax-\frac{1}{8}a-\frac{7}{10}x-\frac{7}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-13)(q-\frac{13}{20})& =(\color{red}{x}+\color{orange}{(-13)}).(\color{green}{q}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(-13)} . \color{green}{(q)} + \color{orange}{(-13)} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{20}x-13q+13.\frac{13}{20}& \text{Uitwerken } \\ & =qx-\frac{13}{20}x-13q+\frac{169}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{15}{12})(q+\frac{-19}{15})& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{15}a-\frac{5}{4}q+\frac{5}{4}.\frac{19}{15}& \text{Uitwerken } \\ & =aq-\frac{19}{15}a-\frac{5}{4}q+\frac{95}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{19}{15}a-\frac{5}{4}q+\frac{19}{12} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-7}{3}+b)(q-\frac{-9}{15})& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{5}b-\frac{7}{3}q-\frac{7}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =bq+\frac{3}{5}b-\frac{7}{3}q-\frac{21}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{5}b-\frac{7}{3}q-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-6}{20})(\frac{17}{7}-p)& =(\color{red}{b}+\color{orange}{\frac{3}{10}}).(\color{green}{-p}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{7}b-\frac{3}{10}p+\frac{3}{10}.\frac{17}{7}& \text{Uitwerken } \\ & =-bp+\frac{17}{7}b-\frac{3}{10}p+\frac{51}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{4}{2})(\frac{18}{9}-b)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bq+2q+2b-2.2& \text{Uitwerken } \\ & =-bq+2q+2b-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-3}{16})(a-\frac{7}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{16}}).(\color{green}{a}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{18}b-\frac{3}{16}a+\frac{3}{16}.\frac{7}{18}& \text{Uitwerken } \\ & =ab-\frac{7}{18}b-\frac{3}{16}a+\frac{21}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{7}{18}b-\frac{3}{16}a+\frac{7}{96} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-6}{15})(\frac{18}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bb+2b-\frac{2}{5}b+\frac{2}{5}.2& \text{Uitwerken } \\ & =-b^2+(2+(\frac{-2}{5}))b+(\frac{-4}{5}) & \text{Neem samen} \\ &=-b^2+\frac{8}{5}b+(\frac{-4}{5}) & \text{Maak de som} \\\end{align}\)
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