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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{17}+a)(\frac{16}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{17}}).(\color{green}{b}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{19}{17})} . \color{green}{(b)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ab+8a+\frac{19}{17}b+\frac{19}{17}.8& \text{Uitwerken } \\ & =ab+8a+\frac{19}{17}b+\frac{152}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{20}-x)(\frac{3}{10}-a)& =(\color{red}{-x}+\color{orange}{\frac{-7}{10}}).(\color{green}{-a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{10}x+\frac{7}{10}a-\frac{7}{10}.\frac{3}{10}& \text{Uitwerken } \\ & =ax-\frac{3}{10}x+\frac{7}{10}a-\frac{21}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{20}{8})(\frac{1}{3}-x)& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{-x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{3}q+\frac{5}{2}x-\frac{5}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =-qx+\frac{1}{3}q+\frac{5}{2}x-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{20}{17})(\frac{-8}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{20}{17}}).(\color{green}{-a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{20}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{9}b-\frac{20}{17}a-\frac{20}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =-ab-\frac{4}{9}b-\frac{20}{17}a-\frac{80}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{10}+a)(\frac{-6}{15}+q)& =(\color{red}{a}+\color{orange}{\frac{-3}{10}}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{5}a-\frac{3}{10}q+\frac{3}{10}.\frac{2}{5}& \text{Uitwerken } \\ & =aq-\frac{2}{5}a-\frac{3}{10}q+\frac{6}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{5}a-\frac{3}{10}q+\frac{3}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-12}{15})(x-\frac{-4}{5})& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{5}a-\frac{4}{5}x-\frac{4}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =ax+\frac{4}{5}a-\frac{4}{5}x-\frac{16}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{20}+a)(\frac{-12}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{7}a+\frac{1}{2}b-\frac{1}{2}.\frac{12}{7}& \text{Uitwerken } \\ & =ab-\frac{12}{7}a+\frac{1}{2}b-\frac{12}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{12}{7}a+\frac{1}{2}b-\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{10}+x)(\frac{-9}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{5}x+\frac{6}{5}x-\frac{6}{5}.\frac{9}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{5})+\frac{6}{5})x-(\frac{-54}{25}) & \text{Neem samen} \\ &=x^2-\frac{3}{5}x-(\frac{-54}{25}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-1}{10})(\frac{-13}{9}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{-p}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{13}{9}p-\frac{1}{10}p-\frac{1}{10}.\frac{13}{9}& \text{Uitwerken } \\ & =-p^2+((\frac{-13}{9})+(\frac{-1}{10}))p-\frac{13}{90} & \text{Neem samen} \\ &=-p^2-\frac{139}{90}p-\frac{13}{90} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a+\frac{17}{16})(b+\frac{3}{6})& =(\color{red}{a}+\color{orange}{\frac{17}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{17}{16})} . \color{green}{(b)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a+\frac{17}{16}b+\frac{17}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a+\frac{17}{16}b+\frac{17}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-9}{6})(\frac{12}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p-\frac{3}{2}b-\frac{3}{2}.2& \text{Uitwerken } \\ & =bp+2p-\frac{3}{2}b-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+2p-\frac{3}{2}b-3 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{4}+a)(\frac{11}{14}+a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{14}a+1a+1.\frac{11}{14}& \text{Uitwerken } \\ & =a^2+(\frac{11}{14}+1)a+\frac{11}{14} & \text{Neem samen} \\ &=a^2+\frac{25}{14}a+\frac{11}{14} & \text{Maak de som} \\\end{align}\)
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