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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{7}-a)(\frac{-12}{16}-x)& =(\color{red}{-a}+\color{orange}{\frac{11}{7}}).(\color{green}{-x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{11}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}a-\frac{11}{7}x-\frac{11}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}a-\frac{11}{7}x-\frac{33}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-8}{3})(\frac{19}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{4}b-\frac{8}{3}x-\frac{8}{3}.\frac{19}{4}& \text{Uitwerken } \\ & =bx+\frac{19}{4}b-\frac{8}{3}x-\frac{152}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{19}{4}b-\frac{8}{3}x-\frac{38}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{14}{7})(\frac{3}{2}+q)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}a-2q-2.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}a-2q-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{2}a-2q-3 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{9}-a)(\frac{-3}{10}-x)& =(\color{red}{-a}+\color{orange}{\frac{20}{9}}).(\color{green}{-x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{10}a-\frac{20}{9}x-\frac{20}{9}.\frac{3}{10}& \text{Uitwerken } \\ & =ax+\frac{3}{10}a-\frac{20}{9}x-\frac{60}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{10}a-\frac{20}{9}x-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{9}+x)(q+\frac{15}{8})& =(\color{red}{x}+\color{orange}{\frac{11}{9}}).(\color{green}{q}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{15}{8}x+\frac{11}{9}q+\frac{11}{9}.\frac{15}{8}& \text{Uitwerken } \\ & =qx+\frac{15}{8}x+\frac{11}{9}q+\frac{165}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{15}{8}x+\frac{11}{9}q+\frac{55}{24} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{10}{11})(\frac{16}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{-10}{11}}).(\color{green}{p}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{16}{9}b-\frac{10}{11}p-\frac{10}{11}.\frac{16}{9}& \text{Uitwerken } \\ & =bp+\frac{16}{9}b-\frac{10}{11}p-\frac{160}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-14}{6})(\frac{17}{3}-a)& =(\color{red}{p}+\color{orange}{\frac{7}{3}}).(\color{green}{-a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{3}p-\frac{7}{3}a+\frac{7}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =-ap+\frac{17}{3}p-\frac{7}{3}a+\frac{119}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{9}{17})(\frac{-9}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{17}}).(\color{green}{-q}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{2}b-\frac{9}{17}q-\frac{9}{17}.\frac{9}{2}& \text{Uitwerken } \\ & =-bq-\frac{9}{2}b-\frac{9}{17}q-\frac{81}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{8}-a)(\frac{18}{17}-b)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{17}a-1b+1.\frac{18}{17}& \text{Uitwerken } \\ & =ab-\frac{18}{17}a-1b+\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-15}{6})(\frac{12}{2}+q)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = qq+6q+\frac{5}{2}q+\frac{5}{2}.6& \text{Uitwerken } \\ & =q^2+(6+\frac{5}{2})q+\frac{30}{2} & \text{Neem samen} \\ &=q^2+\frac{17}{2}q+\frac{30}{2} & \text{Maak de som} \\ &=q^2+\frac{17}{2}q+15 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-10}{2})(\frac{-20}{5}-a)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -aq-4q-5a-5.4& \text{Uitwerken } \\ & =-aq-4q-5a-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{11}-p)(a+\frac{2}{16})& =(\color{red}{-p}+\color{orange}{\frac{4}{11}}).(\color{green}{a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{4}{11})} . \color{green}{(a)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{8}p+\frac{4}{11}a+\frac{4}{11}.\frac{1}{8}& \text{Uitwerken } \\ & =-ap-\frac{1}{8}p+\frac{4}{11}a+\frac{4}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{8}p+\frac{4}{11}a+\frac{1}{22} & \text{Vereenvoudig} \\\end{align}\)
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