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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{13}{10})(b-\frac{16}{13})& =(\color{red}{x}+\color{orange}{\frac{13}{10}}).(\color{green}{b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{13}{10})} . \color{green}{(b)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{13}x+\frac{13}{10}b-\frac{13}{10}.\frac{16}{13}& \text{Uitwerken } \\ & =bx-\frac{16}{13}x+\frac{13}{10}b-\frac{208}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{16}{13}x+\frac{13}{10}b-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{16}-a)(b-\frac{8}{16})& =(\color{red}{-a}+\color{orange}{\frac{11}{16}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{11}{16})} . \color{green}{(b)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{2}a+\frac{11}{16}b-\frac{11}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab+\frac{1}{2}a+\frac{11}{16}b-\frac{11}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-2}{14}-p)(\frac{6}{18}-b)& =(\color{red}{-p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{3}p+\frac{1}{7}b-\frac{1}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =bp-\frac{1}{3}p+\frac{1}{7}b-\frac{1}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{10}{11}+p)(q-\frac{-1}{6})& =(\color{red}{p}+\color{orange}{\frac{10}{11}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{6}p+\frac{10}{11}q+\frac{10}{11}.\frac{1}{6}& \text{Uitwerken } \\ & =pq+\frac{1}{6}p+\frac{10}{11}q+\frac{10}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{6}p+\frac{10}{11}q+\frac{5}{33} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{8}{16})(x-\frac{-14}{10})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{5}p-\frac{1}{2}x-\frac{1}{2}.\frac{7}{5}& \text{Uitwerken } \\ & =px+\frac{7}{5}p-\frac{1}{2}x-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{11}+q)(a-\frac{-16}{20})& =(\color{red}{q}+\color{orange}{\frac{20}{11}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{20}{11})} . \color{green}{(a)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{5}q+\frac{20}{11}a+\frac{20}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =aq+\frac{4}{5}q+\frac{20}{11}a+\frac{80}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{4}{5}q+\frac{20}{11}a+\frac{16}{11} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{6}{14})(x+\frac{-20}{14})& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{7}q-\frac{3}{7}x+\frac{3}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =qx-\frac{10}{7}q-\frac{3}{7}x+\frac{30}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{2}{3})(\frac{-4}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{5}q+\frac{2}{3}a+\frac{2}{3}.\frac{2}{5}& \text{Uitwerken } \\ & =-aq-\frac{2}{5}q+\frac{2}{3}a+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-(-5))(\frac{-12}{16}-a)& =(\color{red}{x}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{4}x-5a-5.\frac{3}{4}& \text{Uitwerken } \\ & =-ax-\frac{3}{4}x-5a-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{13}{8})(\frac{16}{10}+q)& =(\color{red}{p}+\color{orange}{\frac{-13}{8}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{5}p-\frac{13}{8}q-\frac{13}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =pq+\frac{8}{5}p-\frac{13}{8}q-\frac{104}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{5}p-\frac{13}{8}q-\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-14}{18})(\frac{12}{11}+q)& =(\color{red}{b}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{12}{11}b+\frac{7}{9}q+\frac{7}{9}.\frac{12}{11}& \text{Uitwerken } \\ & =bq+\frac{12}{11}b+\frac{7}{9}q+\frac{84}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{12}{11}b+\frac{7}{9}q+\frac{28}{33} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-16}{16})(p-\frac{-15}{8})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{8}p-1p-1.\frac{15}{8}& \text{Uitwerken } \\ & =p^2+(\frac{15}{8}+(-1))p-(\frac{-15}{8}) & \text{Neem samen} \\ &=p^2+\frac{7}{8}p-(\frac{-15}{8}) & \text{Maak de som} \\\end{align}\)
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