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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{4}{13})(\frac{-5}{20}-b)& =(\color{red}{a}+\color{orange}{\frac{4}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{4}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{4}a-\frac{4}{13}b-\frac{4}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =-ab-\frac{1}{4}a-\frac{4}{13}b-\frac{4}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{1}{4}a-\frac{4}{13}b-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{10}-q)(a-\frac{18}{17})& =(\color{red}{-q}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{18}{17}q+\frac{1}{5}a-\frac{1}{5}.\frac{18}{17}& \text{Uitwerken } \\ & =-aq+\frac{18}{17}q+\frac{1}{5}a-\frac{18}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-10}{7})(\frac{-14}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{-p}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{2}a+\frac{10}{7}p+\frac{10}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =-ap-\frac{7}{2}a+\frac{10}{7}p+\frac{70}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{2}a+\frac{10}{7}p+5 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{5}+x)(\frac{-4}{11}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{5}}).(\color{green}{-x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{4}{11}x-\frac{9}{5}x-\frac{9}{5}.\frac{4}{11}& \text{Uitwerken } \\ & =-x^2+((\frac{-4}{11})+(\frac{-9}{5}))x-\frac{36}{55} & \text{Neem samen} \\ &=-x^2-\frac{119}{55}x-\frac{36}{55} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{17}+x)(\frac{-20}{12}-x)& =(\color{red}{x}+\color{orange}{\frac{-14}{17}}).(\color{green}{-x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{3}x+\frac{14}{17}x+\frac{14}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{3})+\frac{14}{17})x+(\frac{-70}{51}) & \text{Neem samen} \\ &=-x^2-\frac{43}{51}x+(\frac{-70}{51}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b+\frac{10}{4})(\frac{13}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{a}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{15}b+\frac{5}{2}a+\frac{5}{2}.\frac{13}{15}& \text{Uitwerken } \\ & =ab+\frac{13}{15}b+\frac{5}{2}a+\frac{65}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{13}{15}b+\frac{5}{2}a+\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{1}{14})(\frac{-17}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{14}}).(\color{green}{x}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{11}q-\frac{1}{14}x+\frac{1}{14}.\frac{17}{11}& \text{Uitwerken } \\ & =qx-\frac{17}{11}q-\frac{1}{14}x+\frac{17}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{16}{14})(q-\frac{-2}{19})& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{19}x-\frac{8}{7}q-\frac{8}{7}.\frac{2}{19}& \text{Uitwerken } \\ & =qx+\frac{2}{19}x-\frac{8}{7}q-\frac{16}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{15}+p)(\frac{18}{15}-q)& =(\color{red}{p}+\color{orange}{\frac{-4}{15}}).(\color{green}{-q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{6}{5}p+\frac{4}{15}q-\frac{4}{15}.\frac{6}{5}& \text{Uitwerken } \\ & =-pq+\frac{6}{5}p+\frac{4}{15}q-\frac{24}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{6}{5}p+\frac{4}{15}q-\frac{8}{25} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{18}-x)(a+\frac{-6}{17})& =(\color{red}{-x}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{6}{17}x-\frac{5}{6}a+\frac{5}{6}.\frac{6}{17}& \text{Uitwerken } \\ & =-ax+\frac{6}{17}x-\frac{5}{6}a+\frac{30}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{6}{17}x-\frac{5}{6}a+\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{12}-q)(\frac{-15}{19}-x)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{15}{19}q-\frac{1}{2}x-\frac{1}{2}.\frac{15}{19}& \text{Uitwerken } \\ & =qx+\frac{15}{19}q-\frac{1}{2}x-\frac{15}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{6}-q)(\frac{-18}{9}-q)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qq+2q+1q+1.2& \text{Uitwerken } \\ & =q^2+(2+1)q+2 & \text{Neem samen} \\ &=q^2+3q+2 & \text{Maak de som} \\\end{align}\)
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