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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-17}{8})(\frac{-4}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{17}{8}}).(\color{green}{-x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{17}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{11}a-\frac{17}{8}x-\frac{17}{8}.\frac{4}{11}& \text{Uitwerken } \\ & =-ax-\frac{4}{11}a-\frac{17}{8}x-\frac{68}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{4}{11}a-\frac{17}{8}x-\frac{17}{22} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{13}-b)(\frac{-6}{12}-q)& =(\color{red}{-b}+\color{orange}{\frac{-5}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{2}b+\frac{5}{13}q+\frac{5}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =bq+\frac{1}{2}b+\frac{5}{13}q+\frac{5}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{11}{4})(q+\frac{-13}{3})& =(\color{red}{x}+\color{orange}{\frac{11}{4}}).(\color{green}{q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{11}{4})} . \color{green}{(q)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{3}x+\frac{11}{4}q-\frac{11}{4}.\frac{13}{3}& \text{Uitwerken } \\ & =qx-\frac{13}{3}x+\frac{11}{4}q-\frac{143}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{20}-a)(\frac{-11}{3}+q)& =(\color{red}{-a}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{11}{3}a+\frac{3}{10}q-\frac{3}{10}.\frac{11}{3}& \text{Uitwerken } \\ & =-aq+\frac{11}{3}a+\frac{3}{10}q-\frac{33}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{11}{3}a+\frac{3}{10}q-\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{17}-a)(q-\frac{-18}{13})& =(\color{red}{-a}+\color{orange}{\frac{-16}{17}}).(\color{green}{q}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{18}{13}a-\frac{16}{17}q-\frac{16}{17}.\frac{18}{13}& \text{Uitwerken } \\ & =-aq-\frac{18}{13}a-\frac{16}{17}q-\frac{288}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{3}-q)(\frac{13}{9}+p)& =(\color{red}{-q}+\color{orange}{\frac{-20}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{9}q-\frac{20}{3}p-\frac{20}{3}.\frac{13}{9}& \text{Uitwerken } \\ & =-pq-\frac{13}{9}q-\frac{20}{3}p-\frac{260}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-4}{20})(\frac{16}{20}+b)& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{5}b+\frac{1}{5}b+\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =b^2+(\frac{4}{5}+\frac{1}{5})b+\frac{4}{25} & \text{Neem samen} \\ &=b^2+\frac{5}{5}b+\frac{4}{25} & \text{Maak de som} \\ &=b^2+1b+\frac{4}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{12}+q)(\frac{9}{15}+q)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{5}q-\frac{4}{3}q-\frac{4}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =q^2+(\frac{3}{5}+(\frac{-4}{3}))q-(\frac{-12}{15}) & \text{Neem samen} \\ &=q^2-\frac{11}{15}q-(\frac{-12}{15}) & \text{Maak de som} \\ &=q^2-\frac{11}{15}q+\frac{4}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(b+\frac{19}{11})(a-\frac{19}{13})& =(\color{red}{b}+\color{orange}{\frac{19}{11}}).(\color{green}{a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{19}{11})} . \color{green}{(a)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{13}b+\frac{19}{11}a-\frac{19}{11}.\frac{19}{13}& \text{Uitwerken } \\ & =ab-\frac{19}{13}b+\frac{19}{11}a-\frac{361}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{2}{16}+x)(\frac{-17}{18}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{18}x+\frac{1}{8}a-\frac{1}{8}.\frac{17}{18}& \text{Uitwerken } \\ & =ax-\frac{17}{18}x+\frac{1}{8}a-\frac{17}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-13}{16})(\frac{-6}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{13}{16}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{13}{16})} . \color{green}{(q)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}b+\frac{13}{16}q-\frac{13}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}b+\frac{13}{16}q-\frac{13}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{10}+a)(q+\frac{10}{7})& =(\color{red}{a}+\color{orange}{\frac{7}{10}}).(\color{green}{q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{10}{7}a+\frac{7}{10}q+\frac{7}{10}.\frac{10}{7}& \text{Uitwerken } \\ & =aq+\frac{10}{7}a+\frac{7}{10}q+\frac{70}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{10}{7}a+\frac{7}{10}q+1 & \text{Vereenvoudig} \\\end{align}\)
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