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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{10}{13})(q-\frac{2}{11})& =(\color{red}{b}+\color{orange}{\frac{-10}{13}}).(\color{green}{q}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{11}b-\frac{10}{13}q+\frac{10}{13}.\frac{2}{11}& \text{Uitwerken } \\ & =bq-\frac{2}{11}b-\frac{10}{13}q+\frac{20}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{11}{12})(p+\frac{-6}{16})& =(\color{red}{q}+\color{orange}{\frac{-11}{12}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{8}q-\frac{11}{12}p+\frac{11}{12}.\frac{3}{8}& \text{Uitwerken } \\ & =pq-\frac{3}{8}q-\frac{11}{12}p+\frac{33}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{8}q-\frac{11}{12}p+\frac{11}{32} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-12}{20})(\frac{-13}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{17}a-\frac{3}{5}p+\frac{3}{5}.\frac{13}{17}& \text{Uitwerken } \\ & =ap-\frac{13}{17}a-\frac{3}{5}p+\frac{39}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(8+a)(p+\frac{-16}{5})& =(\color{red}{a}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{5}a+8p-8.\frac{16}{5}& \text{Uitwerken } \\ & =ap-\frac{16}{5}a+8p-\frac{128}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-9}{13})(p-\frac{-3}{19})& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{p}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{19}a-\frac{9}{13}p-\frac{9}{13}.\frac{3}{19}& \text{Uitwerken } \\ & =ap+\frac{3}{19}a-\frac{9}{13}p-\frac{27}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{14}{16})(\frac{2}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{-7}{8}}).(\color{green}{-a}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{7}p+\frac{7}{8}a-\frac{7}{8}.\frac{1}{7}& \text{Uitwerken } \\ & =-ap+\frac{1}{7}p+\frac{7}{8}a-\frac{7}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{7}p+\frac{7}{8}a-\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{15}{13})(q-\frac{-1}{18})& =(\color{red}{q}+\color{orange}{\frac{-15}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{18}q-\frac{15}{13}q-\frac{15}{13}.\frac{1}{18}& \text{Uitwerken } \\ & =q^2+(\frac{1}{18}+(\frac{-15}{13}))q-(\frac{-15}{234}) & \text{Neem samen} \\ &=q^2-\frac{257}{234}q-(\frac{-15}{234}) & \text{Maak de som} \\ &=q^2-\frac{257}{234}q+\frac{5}{78} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{16}-q)(x+\frac{13}{14})& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{14}q-\frac{1}{2}x-\frac{1}{2}.\frac{13}{14}& \text{Uitwerken } \\ & =-qx-\frac{13}{14}q-\frac{1}{2}x-\frac{13}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{3}{16})(\frac{-3}{6}+b)& =(\color{red}{q}+\color{orange}{\frac{3}{16}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{16})} . \color{green}{(b)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{2}q+\frac{3}{16}b-\frac{3}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =bq-\frac{1}{2}q+\frac{3}{16}b-\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{4}{6})(\frac{20}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{20}{17}p+\frac{2}{3}p-\frac{2}{3}.\frac{20}{17}& \text{Uitwerken } \\ & =-p^2+(\frac{20}{17}+\frac{2}{3})p-\frac{40}{51} & \text{Neem samen} \\ &=-p^2+\frac{94}{51}p-\frac{40}{51} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-9}{16})(b-\frac{-10}{2})& =(\color{red}{q}+\color{orange}{\frac{-9}{16}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{-9}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bq+5q-\frac{9}{16}b-\frac{9}{16}.5& \text{Uitwerken } \\ & =bq+5q-\frac{9}{16}b-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{9}+x)(x+\frac{-9}{3})& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = xx-3x-\frac{5}{3}x+\frac{5}{3}.3& \text{Uitwerken } \\ & =x^2+((-3)+(\frac{-5}{3}))x+\frac{15}{3} & \text{Neem samen} \\ &=x^2-\frac{14}{3}x+\frac{15}{3} & \text{Maak de som} \\ &=x^2-\frac{14}{3}x+5 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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