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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{20}{16})(b+\frac{-17}{5})& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{5}b+\frac{5}{4}b-\frac{5}{4}.\frac{17}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{5})+\frac{5}{4})b-(\frac{-85}{20}) & \text{Neem samen} \\ &=b^2-\frac{43}{20}b-(\frac{-85}{20}) & \text{Maak de som} \\ &=b^2-\frac{43}{20}b+\frac{17}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{6}-q)(\frac{-13}{11}-a)& =(\color{red}{-q}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{11}q+\frac{1}{6}a+\frac{1}{6}.\frac{13}{11}& \text{Uitwerken } \\ & =aq+\frac{13}{11}q+\frac{1}{6}a+\frac{13}{66} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{10}+b)(p+\frac{-17}{10})& =(\color{red}{b}+\color{orange}{\frac{13}{10}}).(\color{green}{p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{13}{10})} . \color{green}{(p)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{10}b+\frac{13}{10}p-\frac{13}{10}.\frac{17}{10}& \text{Uitwerken } \\ & =bp-\frac{17}{10}b+\frac{13}{10}p-\frac{221}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{10}+b)(x-\frac{-19}{16})& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{x}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{16}b-\frac{6}{5}x-\frac{6}{5}.\frac{19}{16}& \text{Uitwerken } \\ & =bx+\frac{19}{16}b-\frac{6}{5}x-\frac{114}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{19}{16}b-\frac{6}{5}x-\frac{57}{40} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{2}{16}+a)(\frac{20}{15}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{3}a+\frac{1}{8}x+\frac{1}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =ax+\frac{4}{3}a+\frac{1}{8}x+\frac{4}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{3}a+\frac{1}{8}x+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{16}-a)(x+\frac{6}{2})& =(\color{red}{-a}+\color{orange}{\frac{-1}{16}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ax-3a-\frac{1}{16}x-\frac{1}{16}.3& \text{Uitwerken } \\ & =-ax-3a-\frac{1}{16}x-\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-7}{2})(\frac{18}{5}+x)& =(\color{red}{a}+\color{orange}{\frac{-7}{2}}).(\color{green}{x}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{18}{5}a-\frac{7}{2}x-\frac{7}{2}.\frac{18}{5}& \text{Uitwerken } \\ & =ax+\frac{18}{5}a-\frac{7}{2}x-\frac{126}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{18}{5}a-\frac{7}{2}x-\frac{63}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{11}+p)(a+\frac{-14}{20})& =(\color{red}{p}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{10}p-\frac{9}{11}a+\frac{9}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =ap-\frac{7}{10}p-\frac{9}{11}a+\frac{63}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{12}{18}+a)(\frac{-12}{7}-p)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-p}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{12}{7}a-\frac{2}{3}p-\frac{2}{3}.\frac{12}{7}& \text{Uitwerken } \\ & =-ap-\frac{12}{7}a-\frac{2}{3}p-\frac{24}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{12}{7}a-\frac{2}{3}p-\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{13}{17})(a+\frac{-6}{15})& =(\color{red}{q}+\color{orange}{\frac{-13}{17}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{5}q-\frac{13}{17}a+\frac{13}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =aq-\frac{2}{5}q-\frac{13}{17}a+\frac{26}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{10}+b)(\frac{-1}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{6}{5}}).(\color{green}{-a}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{11}b-\frac{6}{5}a-\frac{6}{5}.\frac{1}{11}& \text{Uitwerken } \\ & =-ab-\frac{1}{11}b-\frac{6}{5}a-\frac{6}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-18}{20})(q+\frac{-20}{3})& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{q}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{3}a-\frac{9}{10}q+\frac{9}{10}.\frac{20}{3}& \text{Uitwerken } \\ & =aq-\frac{20}{3}a-\frac{9}{10}q+\frac{180}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{20}{3}a-\frac{9}{10}q+6 & \text{Vereenvoudig} \\\end{align}\)
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