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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{8}+x)(a-\frac{14}{9})& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{a}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{9}x+\frac{9}{8}a-\frac{9}{8}.\frac{14}{9}& \text{Uitwerken } \\ & =ax-\frac{14}{9}x+\frac{9}{8}a-\frac{126}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{14}{9}x+\frac{9}{8}a-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{-9}{16})(\frac{-12}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{-9}{16}}).(\color{green}{-q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{7}x+\frac{9}{16}q+\frac{9}{16}.\frac{6}{7}& \text{Uitwerken } \\ & =-qx-\frac{6}{7}x+\frac{9}{16}q+\frac{54}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{7}x+\frac{9}{16}q+\frac{27}{56} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-4}{9})(a-\frac{-18}{14})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{7}a+\frac{4}{9}a+\frac{4}{9}.\frac{9}{7}& \text{Uitwerken } \\ & =a^2+(\frac{9}{7}+\frac{4}{9})a+\frac{36}{63} & \text{Neem samen} \\ &=a^2+\frac{109}{63}a+\frac{36}{63} & \text{Maak de som} \\ &=a^2+\frac{109}{63}a+\frac{4}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{11}+x)(x-\frac{8}{14})& =(\color{red}{x}+\color{orange}{\frac{-19}{11}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{7}x-\frac{19}{11}x+\frac{19}{11}.\frac{4}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{7})+(\frac{-19}{11}))x+\frac{76}{77} & \text{Neem samen} \\ &=x^2-\frac{177}{77}x+\frac{76}{77} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(9+b)(q+\frac{-13}{13})& =(\color{red}{b}+\color{orange}{9}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b+9q-9.1& \text{Uitwerken } \\ & =bq-1b+9q-9 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{7}-x)(p-\frac{10}{7})& =(\color{red}{-x}+\color{orange}{\frac{6}{7}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{7}x+\frac{6}{7}p-\frac{6}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =-px+\frac{10}{7}x+\frac{6}{7}p-\frac{60}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{10}+q)(\frac{19}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{19}{10}}).(\color{green}{-a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{4}q-\frac{19}{10}a+\frac{19}{10}.\frac{19}{4}& \text{Uitwerken } \\ & =-aq+\frac{19}{4}q-\frac{19}{10}a+\frac{361}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-7}{12})(b-\frac{-9}{14})& =(\color{red}{x}+\color{orange}{\frac{7}{12}}).(\color{green}{b}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{7}{12})} . \color{green}{(b)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{14}x+\frac{7}{12}b+\frac{7}{12}.\frac{9}{14}& \text{Uitwerken } \\ & =bx+\frac{9}{14}x+\frac{7}{12}b+\frac{63}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{14}x+\frac{7}{12}b+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{4}-a)(x-\frac{14}{9})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{14}{9}a+\frac{3}{2}x-\frac{3}{2}.\frac{14}{9}& \text{Uitwerken } \\ & =-ax+\frac{14}{9}a+\frac{3}{2}x-\frac{42}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{14}{9}a+\frac{3}{2}x-\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{9}-q)(\frac{-18}{17}-q)& =(\color{red}{-q}+\color{orange}{\frac{-7}{9}}).(\color{green}{-q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{18}{17}q+\frac{7}{9}q+\frac{7}{9}.\frac{18}{17}& \text{Uitwerken } \\ & =q^2+(\frac{18}{17}+\frac{7}{9})q+\frac{126}{153} & \text{Neem samen} \\ &=q^2+\frac{281}{153}q+\frac{126}{153} & \text{Maak de som} \\ &=q^2+\frac{281}{153}q+\frac{14}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{18}+b)(\frac{-8}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ab-4b+\frac{8}{9}a-\frac{8}{9}.4& \text{Uitwerken } \\ & =ab-4b+\frac{8}{9}a-\frac{32}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{7}+q)(\frac{1}{6}+q)& =(\color{red}{q}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{6}q+\frac{10}{7}q+\frac{10}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =q^2+(\frac{1}{6}+\frac{10}{7})q+\frac{10}{42} & \text{Neem samen} \\ &=q^2+\frac{67}{42}q+\frac{10}{42} & \text{Maak de som} \\ &=q^2+\frac{67}{42}q+\frac{5}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-20 20:57:22
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