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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{3}{10})(\frac{5}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{3}{10}}).(\color{green}{-a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{7}b-\frac{3}{10}a+\frac{3}{10}.\frac{5}{7}& \text{Uitwerken } \\ & =-ab+\frac{5}{7}b-\frac{3}{10}a+\frac{15}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{7}b-\frac{3}{10}a+\frac{3}{14} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-19)(\frac{-8}{19}-b)& =(\color{red}{q}+\color{orange}{(-19)}).(\color{green}{-b}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(-19)} . \color{green}{(-b)} + \color{orange}{(-19)} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{19}q+19b+19.\frac{8}{19}& \text{Uitwerken } \\ & =-bq-\frac{8}{19}q+19b+\frac{152}{19} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{19}q+19b+8 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{13}-p)(\frac{14}{17}+x)& =(\color{red}{-p}+\color{orange}{\frac{-16}{13}}).(\color{green}{x}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{14}{17}p-\frac{16}{13}x-\frac{16}{13}.\frac{14}{17}& \text{Uitwerken } \\ & =-px-\frac{14}{17}p-\frac{16}{13}x-\frac{224}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{5}+q)(\frac{-15}{13}-q)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{-q}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{15}{13}q+\frac{2}{5}q+\frac{2}{5}.\frac{15}{13}& \text{Uitwerken } \\ & =-q^2+((\frac{-15}{13})+\frac{2}{5})q+(\frac{-30}{65}) & \text{Neem samen} \\ &=-q^2-\frac{49}{65}q+(\frac{-30}{65}) & \text{Maak de som} \\ &=-q^2-\frac{49}{65}q+(\frac{-6}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-2}{8})(\frac{-5}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a-\frac{1}{4}b+\frac{1}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a-\frac{1}{4}b+\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x+\frac{14}{11})(b+\frac{7}{18})& =(\color{red}{x}+\color{orange}{\frac{14}{11}}).(\color{green}{b}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{18}x+\frac{14}{11}b+\frac{14}{11}.\frac{7}{18}& \text{Uitwerken } \\ & =bx+\frac{7}{18}x+\frac{14}{11}b+\frac{98}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{18}x+\frac{14}{11}b+\frac{49}{99} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{11}{13})(\frac{14}{2}+a)& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(7)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = aq+7q-\frac{11}{13}a-\frac{11}{13}.7& \text{Uitwerken } \\ & =aq+7q-\frac{11}{13}a-\frac{77}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-19}{19})(x+\frac{19}{16})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{19}{16}x-1x-1.\frac{19}{16}& \text{Uitwerken } \\ & =x^2+(\frac{19}{16}+(-1))x-(\frac{-19}{16}) & \text{Neem samen} \\ &=x^2+\frac{3}{16}x-(\frac{-19}{16}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-4}{10})(\frac{-5}{19}+b)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{19}b-\frac{2}{5}b+\frac{2}{5}.\frac{5}{19}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{19})+(\frac{-2}{5}))b+\frac{10}{95} & \text{Neem samen} \\ &=b^2-\frac{63}{95}b+\frac{10}{95} & \text{Maak de som} \\ &=b^2-\frac{63}{95}b+\frac{2}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}((-6)-b)(\frac{-18}{16}-b)& =(\color{red}{-b}+\color{orange}{(-6)}).(\color{green}{-b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(-6)} . \color{green}{(-b)} + \color{orange}{(-6)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{8}b+6b+6.\frac{9}{8}& \text{Uitwerken } \\ & =b^2+(\frac{9}{8}+6)b+\frac{54}{8} & \text{Neem samen} \\ &=b^2+\frac{57}{8}b+\frac{54}{8} & \text{Maak de som} \\ &=b^2+\frac{57}{8}b+\frac{27}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{4}-q)(a+\frac{15}{17})& =(\color{red}{-q}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{17}q+\frac{1}{4}a+\frac{1}{4}.\frac{15}{17}& \text{Uitwerken } \\ & =-aq-\frac{15}{17}q+\frac{1}{4}a+\frac{15}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{20}-x)(\frac{2}{5}-b)& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}x-\frac{3}{4}b+\frac{3}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}x-\frac{3}{4}b+\frac{6}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{5}x-\frac{3}{4}b+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
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