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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{1}{3})(x+\frac{-7}{2})& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{2}b+\frac{1}{3}x-\frac{1}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =bx-\frac{7}{2}b+\frac{1}{3}x-\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{7}{11})(p-\frac{8}{16})& =(\color{red}{p}+\color{orange}{\frac{-7}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{2}p-\frac{7}{11}p+\frac{7}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{2})+(\frac{-7}{11}))p+\frac{7}{22} & \text{Neem samen} \\ &=p^2-\frac{25}{22}p+\frac{7}{22} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{6}+b)(a-\frac{10}{11})& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{11}b+\frac{1}{6}a-\frac{1}{6}.\frac{10}{11}& \text{Uitwerken } \\ & =ab-\frac{10}{11}b+\frac{1}{6}a-\frac{10}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{10}{11}b+\frac{1}{6}a-\frac{5}{33} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{14}-p)(\frac{8}{7}-p)& =(\color{red}{-p}+\color{orange}{\frac{-5}{14}}).(\color{green}{-p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{7}p+\frac{5}{14}p-\frac{5}{14}.\frac{8}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{7})+\frac{5}{14})p-(\frac{-40}{98}) & \text{Neem samen} \\ &=p^2-\frac{11}{14}p-(\frac{-40}{98}) & \text{Maak de som} \\ &=p^2-\frac{11}{14}p+\frac{20}{49} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-8}{11}+q)(\frac{4}{3}-q)& =(\color{red}{q}+\color{orange}{\frac{-8}{11}}).(\color{green}{-q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{3}q+\frac{8}{11}q-\frac{8}{11}.\frac{4}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{3}+\frac{8}{11})q-\frac{32}{33} & \text{Neem samen} \\ &=-q^2+\frac{68}{33}q-\frac{32}{33} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-6}{8}+q)(\frac{-15}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{3}q-\frac{3}{4}a+\frac{3}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =aq-\frac{5}{3}q-\frac{3}{4}a+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{3}q-\frac{3}{4}a+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{16}-b)(\frac{18}{7}+a)& =(\color{red}{-b}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{18}{7}b+\frac{5}{4}a+\frac{5}{4}.\frac{18}{7}& \text{Uitwerken } \\ & =-ab-\frac{18}{7}b+\frac{5}{4}a+\frac{90}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{18}{7}b+\frac{5}{4}a+\frac{45}{14} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{15}+x)(\frac{-6}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{b}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{6}{17}x-\frac{4}{5}b+\frac{4}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =bx-\frac{6}{17}x-\frac{4}{5}b+\frac{24}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-14}{16})(\frac{-18}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{17}a-\frac{7}{8}q+\frac{7}{8}.\frac{18}{17}& \text{Uitwerken } \\ & =aq-\frac{18}{17}a-\frac{7}{8}q+\frac{126}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{18}{17}a-\frac{7}{8}q+\frac{63}{68} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{20}-x)(b+\frac{9}{6})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{2}x+1b+1.\frac{3}{2}& \text{Uitwerken } \\ & =-bx-\frac{3}{2}x+1b+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{17}-p)(q+\frac{-11}{18})& =(\color{red}{-p}+\color{orange}{\frac{-13}{17}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{18}p-\frac{13}{17}q+\frac{13}{17}.\frac{11}{18}& \text{Uitwerken } \\ & =-pq+\frac{11}{18}p-\frac{13}{17}q+\frac{143}{306} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{2}+a)(a-\frac{-6}{13})& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{6}{13}a+\frac{7}{2}a+\frac{7}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =a^2+(\frac{6}{13}+\frac{7}{2})a+\frac{42}{26} & \text{Neem samen} \\ &=a^2+\frac{103}{26}a+\frac{42}{26} & \text{Maak de som} \\ &=a^2+\frac{103}{26}a+\frac{21}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-12 05:17:46
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