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

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  1. \((a+\frac{12}{8})(8+p)\)
  2. \((\frac{5}{6}-p)(q+\frac{20}{7})\)
  3. \((p+\frac{12}{8})(b-\frac{15}{6})\)
  4. \((a+\frac{7}{15})(\frac{6}{16}+p)\)
  5. \((q-\frac{-14}{18})(p-9)\)
  6. \((\frac{-18}{7}+p)(\frac{-19}{7}-p)\)
  7. \((\frac{3}{6}-a)(p-\frac{-5}{6})\)
  8. \((\frac{-16}{6}+b)(\frac{-9}{2}-b)\)
  9. \((\frac{-8}{14}-a)(\frac{12}{18}+q)\)
  10. \((x-5)(p-18)\)
  11. \((\frac{5}{11}+x)(\frac{9}{16}-b)\)
  12. \((\frac{18}{4}+q)(a+\frac{18}{4})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{12}{8})(8+p)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ap+8a+\frac{3}{2}p+\frac{3}{2}.8& \text{Uitwerken } \\ & =ap+8a+\frac{3}{2}p+\frac{24}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+8a+\frac{3}{2}p+12 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{6}-p)(q+\frac{20}{7})& =(\color{red}{-p}+\color{orange}{\frac{5}{6}}).(\color{green}{q}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{20}{7}p+\frac{5}{6}q+\frac{5}{6}.\frac{20}{7}& \text{Uitwerken } \\ & =-pq-\frac{20}{7}p+\frac{5}{6}q+\frac{100}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{20}{7}p+\frac{5}{6}q+\frac{50}{21} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{12}{8})(b-\frac{15}{6})& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{2}p+\frac{3}{2}b-\frac{3}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =bp-\frac{5}{2}p+\frac{3}{2}b-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{7}{15})(\frac{6}{16}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{15}}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{8}a+\frac{7}{15}p+\frac{7}{15}.\frac{3}{8}& \text{Uitwerken } \\ & =ap+\frac{3}{8}a+\frac{7}{15}p+\frac{21}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{8}a+\frac{7}{15}p+\frac{7}{40} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-14}{18})(p-9)& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(\frac{7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = pq-9q+\frac{7}{9}p-\frac{7}{9}.9& \text{Uitwerken } \\ & =pq-9q+\frac{7}{9}p-\frac{63}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-9q+\frac{7}{9}p-7 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{7}+p)(\frac{-19}{7}-p)& =(\color{red}{p}+\color{orange}{\frac{-18}{7}}).(\color{green}{-p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{19}{7}p+\frac{18}{7}p+\frac{18}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-19}{7})+\frac{18}{7})p+(\frac{-342}{49}) & \text{Neem samen} \\ &=-p^2-\frac{1}{7}p+(\frac{-342}{49}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{6}-a)(p-\frac{-5}{6})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{6}a+\frac{1}{2}p+\frac{1}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =-ap-\frac{5}{6}a+\frac{1}{2}p+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{6}+b)(\frac{-9}{2}-b)& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{-b}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{9}{2}b+\frac{8}{3}b+\frac{8}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-9}{2})+\frac{8}{3})b+(\frac{-72}{6}) & \text{Neem samen} \\ &=-b^2-\frac{11}{6}b+(\frac{-72}{6}) & \text{Maak de som} \\ &=-b^2-\frac{11}{6}b+(-12) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{14}-a)(\frac{12}{18}+q)& =(\color{red}{-a}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{3}a-\frac{4}{7}q-\frac{4}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq-\frac{2}{3}a-\frac{4}{7}q-\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-5)(p-18)& =(\color{red}{x}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{(-18)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-18)} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = px-18x-5p+5.18& \text{Uitwerken } \\ & =px-18x-5p+90 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{11}+x)(\frac{9}{16}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{11}}).(\color{green}{-b}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{5}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{16}x-\frac{5}{11}b+\frac{5}{11}.\frac{9}{16}& \text{Uitwerken } \\ & =-bx+\frac{9}{16}x-\frac{5}{11}b+\frac{45}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{18}{4}+q)(a+\frac{18}{4})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{2}q+\frac{9}{2}a+\frac{9}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =aq+\frac{9}{2}q+\frac{9}{2}a+\frac{81}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-07 23:36:58
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