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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{8}-q)(q+\frac{10}{11})& =(\color{red}{-q}+\color{orange}{\frac{9}{8}}).(\color{green}{q}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{10}{11}q+\frac{9}{8}q+\frac{9}{8}.\frac{10}{11}& \text{Uitwerken } \\ & =-q^2+((\frac{-10}{11})+\frac{9}{8})q+(\frac{-90}{88}) & \text{Neem samen} \\ &=-q^2+\frac{19}{88}q+(\frac{-90}{88}) & \text{Maak de som} \\ &=-q^2+\frac{19}{88}q+(\frac{-45}{44}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{7}-x)(\frac{8}{18}+a)& =(\color{red}{-x}+\color{orange}{\frac{20}{7}}).(\color{green}{a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{4}{9}x+\frac{20}{7}a+\frac{20}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =-ax-\frac{4}{9}x+\frac{20}{7}a+\frac{80}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-8}{3})(p+\frac{-10}{7})& =(\color{red}{q}+\color{orange}{\frac{-8}{3}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q-\frac{8}{3}p+\frac{8}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q-\frac{8}{3}p+\frac{80}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-11}{11})(a-\frac{6}{17})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{6}{17}a-1a+1.\frac{6}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-6}{17})+(-1))a+\frac{6}{17} & \text{Neem samen} \\ &=a^2-\frac{23}{17}a+\frac{6}{17} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{19}{16}+p)(\frac{-20}{20}+a)& =(\color{red}{p}+\color{orange}{\frac{19}{16}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p+\frac{19}{16}a-\frac{19}{16}.1& \text{Uitwerken } \\ & =ap-1p+\frac{19}{16}a-\frac{19}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{19}{9})(b-\frac{-7}{6})& =(\color{red}{x}+\color{orange}{\frac{-19}{9}}).(\color{green}{b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{6}x-\frac{19}{9}b-\frac{19}{9}.\frac{7}{6}& \text{Uitwerken } \\ & =bx+\frac{7}{6}x-\frac{19}{9}b-\frac{133}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{4}+p)(\frac{15}{17}-p)& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{-p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{17}p-\frac{9}{4}p+\frac{9}{4}.\frac{15}{17}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{17}+(\frac{-9}{4}))p+(\frac{-135}{68}) & \text{Neem samen} \\ &=-p^2-\frac{93}{68}p+(\frac{-135}{68}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-2}{12}-p)(b-\frac{7}{16})& =(\color{red}{-p}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{16}p-\frac{1}{6}b+\frac{1}{6}.\frac{7}{16}& \text{Uitwerken } \\ & =-bp+\frac{7}{16}p-\frac{1}{6}b+\frac{7}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{7}-p)(b+\frac{18}{5})& =(\color{red}{-p}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{18}{5}p+\frac{6}{7}b+\frac{6}{7}.\frac{18}{5}& \text{Uitwerken } \\ & =-bp-\frac{18}{5}p+\frac{6}{7}b+\frac{108}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-17}{8})(a-\frac{19}{3})& =(\color{red}{x}+\color{orange}{\frac{17}{8}}).(\color{green}{a}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{3}x+\frac{17}{8}a-\frac{17}{8}.\frac{19}{3}& \text{Uitwerken } \\ & =ax-\frac{19}{3}x+\frac{17}{8}a-\frac{323}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{16}+x)(\frac{-16}{15}-a)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{16}{15}x-\frac{3}{4}a-\frac{3}{4}.\frac{16}{15}& \text{Uitwerken } \\ & =-ax-\frac{16}{15}x-\frac{3}{4}a-\frac{48}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{16}{15}x-\frac{3}{4}a-\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{13}{13})(\frac{-13}{9}+b)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{9}p-1b+1.\frac{13}{9}& \text{Uitwerken } \\ & =bp-\frac{13}{9}p-1b+\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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