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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-18}{10})(\frac{-10}{18}-q)& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{-q}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{9}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{9}b-\frac{9}{5}q-\frac{9}{5}.\frac{5}{9}& \text{Uitwerken } \\ & =-bq-\frac{5}{9}b-\frac{9}{5}q-\frac{45}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{9}b-\frac{9}{5}q-1 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b-\frac{11}{3})(p-\frac{20}{15})& =(\color{red}{b}+\color{orange}{\frac{-11}{3}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}b-\frac{11}{3}p+\frac{11}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}b-\frac{11}{3}p+\frac{44}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{7}+p)(\frac{14}{18}+q)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{9}p-2q-2.\frac{7}{9}& \text{Uitwerken } \\ & =pq+\frac{7}{9}p-2q-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{4}+q)((-10)-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -aq-10q+\frac{1}{2}a+\frac{1}{2}.10& \text{Uitwerken } \\ & =-aq-10q+\frac{1}{2}a+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-10q+\frac{1}{2}a+5 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}((-20)+p)(\frac{-18}{5}+b)& =(\color{red}{p}+\color{orange}{(-20)}).(\color{green}{b}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(-20)} . \color{green}{(b)} + \color{orange}{(-20)} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{5}p-20b+20.\frac{18}{5}& \text{Uitwerken } \\ & =bp-\frac{18}{5}p-20b+\frac{360}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{18}{5}p-20b+72 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{10}+q)(q-\frac{14}{7})& =(\color{red}{q}+\color{orange}{\frac{-8}{5}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qq-2q-\frac{8}{5}q+\frac{8}{5}.2& \text{Uitwerken } \\ & =q^2+((-2)+(\frac{-8}{5}))q+\frac{16}{5} & \text{Neem samen} \\ &=q^2-\frac{18}{5}q+\frac{16}{5} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{6}+b)(\frac{18}{7}+q)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{7}b-\frac{3}{2}q-\frac{3}{2}.\frac{18}{7}& \text{Uitwerken } \\ & =bq+\frac{18}{7}b-\frac{3}{2}q-\frac{54}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{7}b-\frac{3}{2}q-\frac{27}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-11}{19})(\frac{18}{20}+q)& =(\color{red}{b}+\color{orange}{\frac{-11}{19}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{10}b-\frac{11}{19}q-\frac{11}{19}.\frac{9}{10}& \text{Uitwerken } \\ & =bq+\frac{9}{10}b-\frac{11}{19}q-\frac{99}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{12}{3})(x-\frac{-11}{12})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{12}p-4x-4.\frac{11}{12}& \text{Uitwerken } \\ & =px+\frac{11}{12}p-4x-\frac{44}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{11}{12}p-4x-\frac{11}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{6}-a)(\frac{17}{2}+a)& =(\color{red}{-a}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{2}a-\frac{10}{3}a-\frac{10}{3}.\frac{17}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{2})+(\frac{-10}{3}))a-\frac{170}{6} & \text{Neem samen} \\ &=-a^2-\frac{71}{6}a-\frac{170}{6} & \text{Maak de som} \\ &=-a^2-\frac{71}{6}a-\frac{85}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-\frac{7}{10})(q+\frac{20}{12})& =(\color{red}{q}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{3}q-\frac{7}{10}q-\frac{7}{10}.\frac{5}{3}& \text{Uitwerken } \\ & =q^2+(\frac{5}{3}+(\frac{-7}{10}))q-(\frac{-35}{30}) & \text{Neem samen} \\ &=q^2+\frac{29}{30}q-(\frac{-35}{30}) & \text{Maak de som} \\ &=q^2+\frac{29}{30}q+\frac{7}{6} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{16}-x)(\frac{-8}{14}-b)& =(\color{red}{-x}+\color{orange}{\frac{1}{16}}).(\color{green}{-b}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{1}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{7}x-\frac{1}{16}b-\frac{1}{16}.\frac{4}{7}& \text{Uitwerken } \\ & =bx+\frac{4}{7}x-\frac{1}{16}b-\frac{4}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{7}x-\frac{1}{16}b-\frac{1}{28} & \text{Vereenvoudig} \\\end{align}\)
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