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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{8}{9})(\frac{14}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{-b}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{4}q+\frac{8}{9}b-\frac{8}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq+\frac{7}{4}q+\frac{8}{9}b-\frac{56}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{4}q+\frac{8}{9}b-\frac{14}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{2}+b)(b-\frac{-12}{17})& =(\color{red}{b}+\color{orange}{\frac{-7}{2}}).(\color{green}{b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{12}{17}b-\frac{7}{2}b-\frac{7}{2}.\frac{12}{17}& \text{Uitwerken } \\ & =b^2+(\frac{12}{17}+(\frac{-7}{2}))b-(\frac{-84}{34}) & \text{Neem samen} \\ &=b^2-\frac{95}{34}b-(\frac{-84}{34}) & \text{Maak de som} \\ &=b^2-\frac{95}{34}b+\frac{42}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(a-\frac{4}{4})(\frac{-12}{2}+p)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ap-6a-1p+1.6& \text{Uitwerken } \\ & =ap-6a-1p+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{-11}{5})(p-\frac{-19}{9})& =(\color{red}{b}+\color{orange}{\frac{11}{5}}).(\color{green}{p}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{9}b+\frac{11}{5}p+\frac{11}{5}.\frac{19}{9}& \text{Uitwerken } \\ & =bp+\frac{19}{9}b+\frac{11}{5}p+\frac{209}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{10}-a)(\frac{6}{6}-p)& =(\color{red}{-a}+\color{orange}{\frac{8}{5}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{8}{5}p+\frac{8}{5}.1& \text{Uitwerken } \\ & =ap-1a-\frac{8}{5}p+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{6}{10})(b+\frac{18}{12})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}p+\frac{3}{5}b+\frac{3}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}p+\frac{3}{5}b+\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{13}{18}+b)(\frac{10}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{13}{18}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{13}{18})} . \color{green}{(q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{3}b+\frac{13}{18}q+\frac{13}{18}.\frac{2}{3}& \text{Uitwerken } \\ & =bq+\frac{2}{3}b+\frac{13}{18}q+\frac{26}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{2}{3}b+\frac{13}{18}q+\frac{13}{27} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-15}{5}-p)(\frac{-18}{10}+p)& =(\color{red}{-p}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{9}{5}p-3p+3.\frac{9}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{9}{5}+(-3))p+(\frac{-27}{5}) & \text{Neem samen} \\ &=-p^2-\frac{6}{5}p+(\frac{-27}{5}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{2}+p)(\frac{9}{17}+p)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{17}p-1p-1.\frac{9}{17}& \text{Uitwerken } \\ & =p^2+(\frac{9}{17}+(-1))p-(\frac{-9}{17}) & \text{Neem samen} \\ &=p^2-\frac{8}{17}p-(\frac{-9}{17}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-7}{2})(a-\frac{2}{19})& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{19}p-\frac{7}{2}a+\frac{7}{2}.\frac{2}{19}& \text{Uitwerken } \\ & =ap-\frac{2}{19}p-\frac{7}{2}a+\frac{14}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{19}p-\frac{7}{2}a+\frac{7}{19} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{17}-q)(a+\frac{-15}{11})& =(\color{red}{-q}+\color{orange}{\frac{5}{17}}).(\color{green}{a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{15}{11}q+\frac{5}{17}a-\frac{5}{17}.\frac{15}{11}& \text{Uitwerken } \\ & =-aq+\frac{15}{11}q+\frac{5}{17}a-\frac{75}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{17}+q)(\frac{-3}{9}+q)& =(\color{red}{q}+\color{orange}{\frac{-13}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{3}q-\frac{13}{17}q+\frac{13}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{3})+(\frac{-13}{17}))q+\frac{13}{51} & \text{Neem samen} \\ &=q^2-\frac{56}{51}q+\frac{13}{51} & \text{Maak de som} \\\end{align}\)
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