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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{1}{10})(\frac{-14}{5}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{10}}).(\color{green}{-a}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{14}{5}q+\frac{1}{10}a+\frac{1}{10}.\frac{14}{5}& \text{Uitwerken } \\ & =-aq-\frac{14}{5}q+\frac{1}{10}a+\frac{14}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{14}{5}q+\frac{1}{10}a+\frac{7}{25} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{20}{11})(p-\frac{2}{4})& =(\color{red}{p}+\color{orange}{\frac{-20}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{2}p-\frac{20}{11}p+\frac{20}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{2})+(\frac{-20}{11}))p+\frac{20}{22} & \text{Neem samen} \\ &=p^2-\frac{51}{22}p+\frac{20}{22} & \text{Maak de som} \\ &=p^2-\frac{51}{22}p+\frac{10}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{14}-b)(\frac{20}{18}-p)& =(\color{red}{-b}+\color{orange}{\frac{1}{7}}).(\color{green}{-p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{9}b-\frac{1}{7}p+\frac{1}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =bp-\frac{10}{9}b-\frac{1}{7}p+\frac{10}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{9}+a)(\frac{-14}{10}-b)& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{5}a+\frac{4}{3}b+\frac{4}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =-ab-\frac{7}{5}a+\frac{4}{3}b+\frac{28}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{18}{15})(\frac{-5}{10}-x)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{2}a+\frac{6}{5}x+\frac{6}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax-\frac{1}{2}a+\frac{6}{5}x+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{1}{2}a+\frac{6}{5}x+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{7}{9})(q+6)& =(\color{red}{b}+\color{orange}{\frac{7}{9}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6b+\frac{7}{9}q+\frac{7}{9}.6& \text{Uitwerken } \\ & =bq+6b+\frac{7}{9}q+\frac{42}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+6b+\frac{7}{9}q+\frac{14}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+17)(\frac{5}{12}-p)& =(\color{red}{x}+\color{orange}{17}).(\color{green}{-p}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(17)} . \color{green}{(-p)} + \color{orange}{(17)} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{12}x-17p+17.\frac{5}{12}& \text{Uitwerken } \\ & =-px+\frac{5}{12}x-17p+\frac{85}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+(-3))(\frac{-14}{16}-x)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{-x}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(-3)} . \color{green}{(-x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{8}p+3x+3.\frac{7}{8}& \text{Uitwerken } \\ & =-px-\frac{7}{8}p+3x+\frac{21}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{12}{15}+x)(b+\frac{-6}{15})& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}x+\frac{4}{5}b-\frac{4}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}x+\frac{4}{5}b-\frac{8}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-16}{20})(x+(-3))& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qx-3q+\frac{4}{5}x-\frac{4}{5}.3& \text{Uitwerken } \\ & =qx-3q+\frac{4}{5}x-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{12}{12}+q)(a-\frac{-11}{14})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{14}q+1a+1.\frac{11}{14}& \text{Uitwerken } \\ & =aq+\frac{11}{14}q+1a+\frac{11}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{18}+a)(\frac{-11}{9}-b)& =(\color{red}{a}+\color{orange}{\frac{7}{18}}).(\color{green}{-b}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{7}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{9}a-\frac{7}{18}b-\frac{7}{18}.\frac{11}{9}& \text{Uitwerken } \\ & =-ab-\frac{11}{9}a-\frac{7}{18}b-\frac{77}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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