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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{7}+q)(\frac{-6}{6}-q)& =(\color{red}{q}+\color{orange}{\frac{-16}{7}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q+\frac{16}{7}q+\frac{16}{7}.1& \text{Uitwerken } \\ & =-q^2+((-1)+\frac{16}{7})q+(\frac{-16}{7}) & \text{Neem samen} \\ &=-q^2+\frac{9}{7}q+(\frac{-16}{7}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p-(-17))(x+\frac{10}{20})& =(\color{red}{p}+\color{orange}{17}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(17)} . \color{green}{(x)} + \color{orange}{(17)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{2}p+17x+17.\frac{1}{2}& \text{Uitwerken } \\ & =px+\frac{1}{2}p+17x+\frac{17}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{20}{18})(\frac{-7}{13}-p)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{-p}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{13}b+\frac{10}{9}p+\frac{10}{9}.\frac{7}{13}& \text{Uitwerken } \\ & =-bp-\frac{7}{13}b+\frac{10}{9}p+\frac{70}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-10}{8}-p)(\frac{-10}{16}-x)& =(\color{red}{-p}+\color{orange}{\frac{-5}{4}}).(\color{green}{-x}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{8}p+\frac{5}{4}x+\frac{5}{4}.\frac{5}{8}& \text{Uitwerken } \\ & =px+\frac{5}{8}p+\frac{5}{4}x+\frac{25}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{18}+q)(q+\frac{19}{16})& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{q}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{16}q-\frac{2}{9}q-\frac{2}{9}.\frac{19}{16}& \text{Uitwerken } \\ & =q^2+(\frac{19}{16}+(\frac{-2}{9}))q-(\frac{-38}{144}) & \text{Neem samen} \\ &=q^2+\frac{139}{144}q-(\frac{-38}{144}) & \text{Maak de som} \\ &=q^2+\frac{139}{144}q+\frac{19}{72} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-12}{9})(\frac{-4}{11}+b)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{11}q-\frac{4}{3}b+\frac{4}{3}.\frac{4}{11}& \text{Uitwerken } \\ & =bq-\frac{4}{11}q-\frac{4}{3}b+\frac{16}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{17}+q)(a+\frac{5}{15})& =(\color{red}{q}+\color{orange}{\frac{-10}{17}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{3}q-\frac{10}{17}a-\frac{10}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =aq+\frac{1}{3}q-\frac{10}{17}a-\frac{10}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{16}{6})(p-\frac{-3}{8})& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{8}b-\frac{8}{3}p-\frac{8}{3}.\frac{3}{8}& \text{Uitwerken } \\ & =bp+\frac{3}{8}b-\frac{8}{3}p-\frac{24}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{8}b-\frac{8}{3}p-1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-6}{12})((-8)+b)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = bp-8p+\frac{1}{2}b-\frac{1}{2}.8& \text{Uitwerken } \\ & =bp-8p+\frac{1}{2}b-\frac{8}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-8p+\frac{1}{2}b-4 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{13}-x)(\frac{13}{8}+b)& =(\color{red}{-x}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{8}x-\frac{4}{13}b-\frac{4}{13}.\frac{13}{8}& \text{Uitwerken } \\ & =-bx-\frac{13}{8}x-\frac{4}{13}b-\frac{52}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{13}{8}x-\frac{4}{13}b-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-9}{20})(b+\frac{-1}{20})& =(\color{red}{a}+\color{orange}{\frac{9}{20}}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{9}{20})} . \color{green}{(b)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{20}a+\frac{9}{20}b-\frac{9}{20}.\frac{1}{20}& \text{Uitwerken } \\ & =ab-\frac{1}{20}a+\frac{9}{20}b-\frac{9}{400} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{6}{17})(\frac{-5}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-6}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{2}a-\frac{6}{17}b+\frac{6}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =ab-\frac{5}{2}a-\frac{6}{17}b+\frac{30}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{2}a-\frac{6}{17}b+\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
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