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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{5}{4})(\frac{-18}{6}+b)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bq-3q+\frac{5}{4}b-\frac{5}{4}.3& \text{Uitwerken } \\ & =bq-3q+\frac{5}{4}b-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{1}{6})(a+\frac{-8}{20})& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{5}a-\frac{1}{6}a+\frac{1}{6}.\frac{2}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{5})+(\frac{-1}{6}))a+\frac{2}{30} & \text{Neem samen} \\ &=a^2-\frac{17}{30}a+\frac{2}{30} & \text{Maak de som} \\ &=a^2-\frac{17}{30}a+\frac{1}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{18}-a)(\frac{7}{18}+b)& =(\color{red}{-a}+\color{orange}{\frac{-7}{18}}).(\color{green}{b}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{18}a-\frac{7}{18}b-\frac{7}{18}.\frac{7}{18}& \text{Uitwerken } \\ & =-ab-\frac{7}{18}a-\frac{7}{18}b-\frac{49}{324} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{10}-a)(\frac{11}{4}-x)& =(\color{red}{-a}+\color{orange}{\frac{3}{5}}).(\color{green}{-x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{4}a-\frac{3}{5}x+\frac{3}{5}.\frac{11}{4}& \text{Uitwerken } \\ & =ax-\frac{11}{4}a-\frac{3}{5}x+\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{16}-x)(\frac{-14}{5}-q)& =(\color{red}{-x}+\color{orange}{\frac{9}{16}}).(\color{green}{-q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{5}x-\frac{9}{16}q-\frac{9}{16}.\frac{14}{5}& \text{Uitwerken } \\ & =qx+\frac{14}{5}x-\frac{9}{16}q-\frac{126}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{14}{5}x-\frac{9}{16}q-\frac{63}{40} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{16}{6})(x-\frac{-16}{19})& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{19}q+\frac{8}{3}x+\frac{8}{3}.\frac{16}{19}& \text{Uitwerken } \\ & =qx+\frac{16}{19}q+\frac{8}{3}x+\frac{128}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{16}+a)(a-\frac{-10}{14})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{7}a+\frac{1}{2}a+\frac{1}{2}.\frac{5}{7}& \text{Uitwerken } \\ & =a^2+(\frac{5}{7}+\frac{1}{2})a+\frac{5}{14} & \text{Neem samen} \\ &=a^2+\frac{17}{14}a+\frac{5}{14} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-6}{14})(\frac{-19}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{4}b+\frac{3}{7}q-\frac{3}{7}.\frac{19}{4}& \text{Uitwerken } \\ & =bq-\frac{19}{4}b+\frac{3}{7}q-\frac{57}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-10}{6})(\frac{18}{4}+x)& =(\color{red}{x}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{2}x+\frac{5}{3}x+\frac{5}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =x^2+(\frac{9}{2}+\frac{5}{3})x+\frac{45}{6} & \text{Neem samen} \\ &=x^2+\frac{37}{6}x+\frac{45}{6} & \text{Maak de som} \\ &=x^2+\frac{37}{6}x+\frac{15}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(b+\frac{9}{4})(\frac{-17}{5}-p)& =(\color{red}{b}+\color{orange}{\frac{9}{4}}).(\color{green}{-p}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{17}{5}b-\frac{9}{4}p-\frac{9}{4}.\frac{17}{5}& \text{Uitwerken } \\ & =-bp-\frac{17}{5}b-\frac{9}{4}p-\frac{153}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{14}-p)(\frac{-14}{17}-b)& =(\color{red}{-p}+\color{orange}{\frac{10}{7}}).(\color{green}{-b}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{17}p-\frac{10}{7}b-\frac{10}{7}.\frac{14}{17}& \text{Uitwerken } \\ & =bp+\frac{14}{17}p-\frac{10}{7}b-\frac{140}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{17}p-\frac{10}{7}b-\frac{20}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{17}{10})(p+\frac{-6}{7})& =(\color{red}{b}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{7}b+\frac{17}{10}p-\frac{17}{10}.\frac{6}{7}& \text{Uitwerken } \\ & =bp-\frac{6}{7}b+\frac{17}{10}p-\frac{102}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{7}b+\frac{17}{10}p-\frac{51}{35} & \text{Vereenvoudig} \\\end{align}\)
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