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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{9}-p)(q-\frac{16}{2})& =(\color{red}{-p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -pq+8p+\frac{1}{3}q-\frac{1}{3}.8& \text{Uitwerken } \\ & =-pq+8p+\frac{1}{3}q-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{18}-q)(b-\frac{-18}{8})& =(\color{red}{-q}+\color{orange}{\frac{-7}{18}}).(\color{green}{b}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{4}q-\frac{7}{18}b-\frac{7}{18}.\frac{9}{4}& \text{Uitwerken } \\ & =-bq-\frac{9}{4}q-\frac{7}{18}b-\frac{63}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{9}{4}q-\frac{7}{18}b-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-9}{5})(\frac{-17}{13}+p)& =(\color{red}{x}+\color{orange}{\frac{9}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{13}x+\frac{9}{5}p-\frac{9}{5}.\frac{17}{13}& \text{Uitwerken } \\ & =px-\frac{17}{13}x+\frac{9}{5}p-\frac{153}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-10}{6})(\frac{-6}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{2}x+\frac{5}{3}q-\frac{5}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =qx-\frac{3}{2}x+\frac{5}{3}q-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{3}{2}x+\frac{5}{3}q-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-9}{10})(\frac{-2}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-9}{10}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{2}a+\frac{9}{10}x+\frac{9}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax-\frac{1}{2}a+\frac{9}{10}x+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{3}-b)(q+\frac{2}{19})& =(\color{red}{-b}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{19}b-\frac{7}{3}q-\frac{7}{3}.\frac{2}{19}& \text{Uitwerken } \\ & =-bq-\frac{2}{19}b-\frac{7}{3}q-\frac{14}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-12}{8}+q)(a-\frac{2}{20})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{10}q-\frac{3}{2}a+\frac{3}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =aq-\frac{1}{10}q-\frac{3}{2}a+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-16}{5})(b+\frac{10}{4})& =(\color{red}{x}+\color{orange}{\frac{16}{5}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{2}x+\frac{16}{5}b+\frac{16}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =bx+\frac{5}{2}x+\frac{16}{5}b+\frac{80}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{2}x+\frac{16}{5}b+8 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{3}+x)(\frac{-8}{8}+q)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-3q+3.1& \text{Uitwerken } \\ & =qx-1x-3q+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-14}{13})(q-\frac{9}{7})& =(\color{red}{q}+\color{orange}{\frac{14}{13}}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{14}{13})} . \color{green}{(q)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{9}{7}q+\frac{14}{13}q-\frac{14}{13}.\frac{9}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-9}{7})+\frac{14}{13})q-(\frac{-126}{91}) & \text{Neem samen} \\ &=q^2-\frac{19}{91}q-(\frac{-126}{91}) & \text{Maak de som} \\ &=q^2-\frac{19}{91}q+\frac{18}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-18}{2})((-9)-a)& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{-a}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-9)} + \color{orange}{(-9)} . \color{green}{(-a)} + \color{orange}{(-9)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -ap-9p+9a+9.9& \text{Uitwerken } \\ & =-ap-9p+9a+81 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-12}{16})(p+\frac{-7}{8})& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{8}p+\frac{3}{4}p-\frac{3}{4}.\frac{7}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{8})+\frac{3}{4})p-(\frac{-21}{32}) & \text{Neem samen} \\ &=p^2-\frac{1}{8}p-(\frac{-21}{32}) & \text{Maak de som} \\\end{align}\)
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