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

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  1. \((q+\frac{13}{2})(a-\frac{7}{2})\)
  2. \((\frac{14}{4}-q)(\frac{6}{17}-b)\)
  3. \((b-\frac{13}{10})(q-9)\)
  4. \((q+\frac{10}{20})(\frac{9}{4}+x)\)
  5. \((\frac{-14}{2}+b)(b-(-20))\)
  6. \((\frac{1}{15}+b)(b-\frac{-10}{12})\)
  7. \((17+q)(\frac{12}{10}-p)\)
  8. \((\frac{1}{14}+q)(\frac{3}{16}+q)\)
  9. \((\frac{4}{16}+a)(a-2)\)
  10. \((\frac{-2}{4}+x)(\frac{4}{15}-x)\)
  11. \((b+\frac{6}{15})(\frac{17}{18}+a)\)
  12. \((\frac{11}{6}+q)((-20)-q)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{13}{2})(a-\frac{7}{2})& =(\color{red}{q}+\color{orange}{\frac{13}{2}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{2}q+\frac{13}{2}a-\frac{13}{2}.\frac{7}{2}& \text{Uitwerken } \\ & =aq-\frac{7}{2}q+\frac{13}{2}a-\frac{91}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{4}-q)(\frac{6}{17}-b)& =(\color{red}{-q}+\color{orange}{\frac{7}{2}}).(\color{green}{-b}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{17}q-\frac{7}{2}b+\frac{7}{2}.\frac{6}{17}& \text{Uitwerken } \\ & =bq-\frac{6}{17}q-\frac{7}{2}b+\frac{42}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{6}{17}q-\frac{7}{2}b+\frac{21}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{13}{10})(q-9)& =(\color{red}{b}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bq-9b-\frac{13}{10}q+\frac{13}{10}.9& \text{Uitwerken } \\ & =bq-9b-\frac{13}{10}q+\frac{117}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{10}{20})(\frac{9}{4}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{4}q+\frac{1}{2}x+\frac{1}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =qx+\frac{9}{4}q+\frac{1}{2}x+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-14}{2}+b)(b-(-20))& =(\color{red}{b}+\color{orange}{(-7)}).(\color{green}{b}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(20)} + \color{orange}{(-7)} . \color{green}{(b)} + \color{orange}{(-7)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = bb+20b-7b-7.20& \text{Uitwerken } \\ & =b^2+(20+(-7))b-(-140) & \text{Neem samen} \\ &=b^2+13b-(-140) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{15}+b)(b-\frac{-10}{12})& =(\color{red}{b}+\color{orange}{\frac{1}{15}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{6}b+\frac{1}{15}b+\frac{1}{15}.\frac{5}{6}& \text{Uitwerken } \\ & =b^2+(\frac{5}{6}+\frac{1}{15})b+\frac{5}{90} & \text{Neem samen} \\ &=b^2+\frac{27}{30}b+\frac{5}{90} & \text{Maak de som} \\ &=b^2+\frac{9}{10}b+\frac{1}{18} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(17+q)(\frac{12}{10}-p)& =(\color{red}{q}+\color{orange}{17}).(\color{green}{-p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(17)} . \color{green}{(-p)} + \color{orange}{(17)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{6}{5}q-17p+17.\frac{6}{5}& \text{Uitwerken } \\ & =-pq+\frac{6}{5}q-17p+\frac{102}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{14}+q)(\frac{3}{16}+q)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{q}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{16}q+\frac{1}{14}q+\frac{1}{14}.\frac{3}{16}& \text{Uitwerken } \\ & =q^2+(\frac{3}{16}+\frac{1}{14})q+\frac{3}{224} & \text{Neem samen} \\ &=q^2+\frac{29}{112}q+\frac{3}{224} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{16}+a)(a-2)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa-2a+\frac{1}{4}a-\frac{1}{4}.2& \text{Uitwerken } \\ & =a^2+((-2)+\frac{1}{4})a-(\frac{-2}{4}) & \text{Neem samen} \\ &=a^2-\frac{7}{4}a-(\frac{-2}{4}) & \text{Maak de som} \\ &=a^2-\frac{7}{4}a+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{4}+x)(\frac{4}{15}-x)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{15}x+\frac{1}{2}x-\frac{1}{2}.\frac{4}{15}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{15}+\frac{1}{2})x-\frac{4}{30} & \text{Neem samen} \\ &=-x^2+\frac{23}{30}x-\frac{4}{30} & \text{Maak de som} \\ &=-x^2+\frac{23}{30}x-\frac{2}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(b+\frac{6}{15})(\frac{17}{18}+a)& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{18}b+\frac{2}{5}a+\frac{2}{5}.\frac{17}{18}& \text{Uitwerken } \\ & =ab+\frac{17}{18}b+\frac{2}{5}a+\frac{34}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{18}b+\frac{2}{5}a+\frac{17}{45} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{6}+q)((-20)-q)& =(\color{red}{q}+\color{orange}{\frac{11}{6}}).(\color{green}{-q}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-20)} + \color{orange}{(\frac{11}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -qq-20q-\frac{11}{6}q-\frac{11}{6}.20& \text{Uitwerken } \\ & =-q^2+((-20)+(\frac{-11}{6}))q-\frac{220}{6} & \text{Neem samen} \\ &=-q^2-\frac{131}{6}q-\frac{220}{6} & \text{Maak de som} \\ &=-q^2-\frac{131}{6}q-\frac{110}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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