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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(11-a)(\frac{6}{6}+q)& =(\color{red}{-a}+\color{orange}{11}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(11)} . \color{green}{(q)} + \color{orange}{(11)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1a+11q+11.1& \text{Uitwerken } \\ & =-aq-1a+11q+11 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-10}{6})(a+\frac{19}{5})& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{5}p+\frac{5}{3}a+\frac{5}{3}.\frac{19}{5}& \text{Uitwerken } \\ & =ap+\frac{19}{5}p+\frac{5}{3}a+\frac{95}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{19}{5}p+\frac{5}{3}a+\frac{19}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-17}{17}-q)(\frac{-12}{11}-p)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{12}{11}q+1p+1.\frac{12}{11}& \text{Uitwerken } \\ & =pq+\frac{12}{11}q+1p+\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{20}-b)(\frac{-18}{8}-a)& =(\color{red}{-b}+\color{orange}{\frac{-1}{5}}).(\color{green}{-a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{4}b+\frac{1}{5}a+\frac{1}{5}.\frac{9}{4}& \text{Uitwerken } \\ & =ab+\frac{9}{4}b+\frac{1}{5}a+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{8}-b)(\frac{-2}{12}-b)& =(\color{red}{-b}+\color{orange}{\frac{7}{8}}).(\color{green}{-b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{6}b-\frac{7}{8}b-\frac{7}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =b^2+(\frac{1}{6}+(\frac{-7}{8}))b-(\frac{-7}{48}) & \text{Neem samen} \\ &=b^2-\frac{17}{24}b-(\frac{-7}{48}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-7}{10})(b+\frac{-12}{9})& =(\color{red}{a}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{3}a-\frac{7}{10}b+\frac{7}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =ab-\frac{4}{3}a-\frac{7}{10}b+\frac{28}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{3}a-\frac{7}{10}b+\frac{14}{15} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-16}{7})(\frac{2}{16}-x)& =(\color{red}{q}+\color{orange}{\frac{-16}{7}}).(\color{green}{-x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{8}q+\frac{16}{7}x-\frac{16}{7}.\frac{1}{8}& \text{Uitwerken } \\ & =-qx+\frac{1}{8}q+\frac{16}{7}x-\frac{16}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{1}{8}q+\frac{16}{7}x-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-5)(\frac{15}{18}+x)& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{6}a-5x-5.\frac{5}{6}& \text{Uitwerken } \\ & =ax+\frac{5}{6}a-5x-\frac{25}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-5}{18})(\frac{-6}{8}+b)& =(\color{red}{p}+\color{orange}{\frac{5}{18}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{4}p+\frac{5}{18}b-\frac{5}{18}.\frac{3}{4}& \text{Uitwerken } \\ & =bp-\frac{3}{4}p+\frac{5}{18}b-\frac{15}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{4}p+\frac{5}{18}b-\frac{5}{24} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-12}{16})(p-\frac{-20}{13})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{13}a+\frac{3}{4}p+\frac{3}{4}.\frac{20}{13}& \text{Uitwerken } \\ & =ap+\frac{20}{13}a+\frac{3}{4}p+\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{13}a+\frac{3}{4}p+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{20}+x)(\frac{14}{8}+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{20}}).(\color{green}{q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{4}x-\frac{3}{20}q-\frac{3}{20}.\frac{7}{4}& \text{Uitwerken } \\ & =qx+\frac{7}{4}x-\frac{3}{20}q-\frac{21}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+(-10))(x+\frac{15}{20})& =(\color{red}{a}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}a-10x-10.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}a-10x-\frac{30}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{3}{4}a-10x-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
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