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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{10}-b)(\frac{-2}{7}-a)& =(\color{red}{-b}+\color{orange}{\frac{-8}{5}}).(\color{green}{-a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{7}b+\frac{8}{5}a+\frac{8}{5}.\frac{2}{7}& \text{Uitwerken } \\ & =ab+\frac{2}{7}b+\frac{8}{5}a+\frac{16}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{10}{17}+b)(\frac{15}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{10}{17}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{10}{17})} . \color{green}{(a)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{4}b+\frac{10}{17}a+\frac{10}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =ab+\frac{5}{4}b+\frac{10}{17}a+\frac{50}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{4}b+\frac{10}{17}a+\frac{25}{34} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{19}+q)(\frac{-10}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{20}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{20}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{2}q-\frac{20}{19}b-\frac{20}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-bq-\frac{1}{2}q-\frac{20}{19}b-\frac{20}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{2}q-\frac{20}{19}b-\frac{10}{19} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{19}{5})(a+\frac{17}{20})& =(\color{red}{b}+\color{orange}{\frac{-19}{5}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{20}b-\frac{19}{5}a-\frac{19}{5}.\frac{17}{20}& \text{Uitwerken } \\ & =ab+\frac{17}{20}b-\frac{19}{5}a-\frac{323}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-5}{15})(b-\frac{11}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{20}p-\frac{1}{3}b+\frac{1}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =bp-\frac{11}{20}p-\frac{1}{3}b+\frac{11}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-(-18))(x-\frac{-7}{12})& =(\color{red}{b}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{12}b+18x+18.\frac{7}{12}& \text{Uitwerken } \\ & =bx+\frac{7}{12}b+18x+\frac{126}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{12}b+18x+\frac{21}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{14}-a)(a-\frac{9}{5})& =(\color{red}{-a}+\color{orange}{\frac{-9}{7}}).(\color{green}{a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{5}a-\frac{9}{7}a+\frac{9}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{5}+(\frac{-9}{7}))a+(\frac{-81}{35}) & \text{Neem samen} \\ &=-a^2+\frac{18}{35}a+(\frac{-81}{35}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{3}{4})(\frac{3}{3}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p+\frac{3}{4}b+\frac{3}{4}.1& \text{Uitwerken } \\ & =bp+1p+\frac{3}{4}b+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-20}{20}-p)(\frac{17}{8}-p)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{8}p+1p-1.\frac{17}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{8})+1)p-(\frac{-17}{8}) & \text{Neem samen} \\ &=p^2-\frac{9}{8}p-(\frac{-17}{8}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{20}+p)(x+\frac{-3}{3})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p-\frac{4}{5}x+\frac{4}{5}.1& \text{Uitwerken } \\ & =px-1p-\frac{4}{5}x+\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{18}-a)(q-\frac{-20}{13})& =(\color{red}{-a}+\color{orange}{\frac{-13}{18}}).(\color{green}{q}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{20}{13}a-\frac{13}{18}q-\frac{13}{18}.\frac{20}{13}& \text{Uitwerken } \\ & =-aq-\frac{20}{13}a-\frac{13}{18}q-\frac{260}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{20}{13}a-\frac{13}{18}q-\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q+\frac{1}{17})(q+\frac{-15}{17})& =(\color{red}{q}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{17}q+\frac{1}{17}q-\frac{1}{17}.\frac{15}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{17})+\frac{1}{17})q-(\frac{-15}{289}) & \text{Neem samen} \\ &=q^2-\frac{14}{17}q-(\frac{-15}{289}) & \text{Maak de som} \\\end{align}\)
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