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

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  1. \((\frac{16}{20}+b)(b-\frac{-15}{8})\)
  2. \((a-\frac{-15}{8})(x-\frac{-8}{17})\)
  3. \((\frac{20}{11}+p)(b-\frac{-4}{5})\)
  4. \((x-\frac{-17}{9})(a+\frac{-14}{15})\)
  5. \((\frac{-18}{6}-a)(\frac{4}{17}+b)\)
  6. \((\frac{-7}{19}-b)(\frac{-10}{14}+q)\)
  7. \((p-\frac{-2}{12})(b-\frac{6}{17})\)
  8. \((\frac{13}{18}+x)(p+\frac{4}{6})\)
  9. \((p+\frac{-14}{16})(\frac{20}{11}+x)\)
  10. \((\frac{20}{16}+b)(\frac{-4}{17}-p)\)
  11. \((q+\frac{6}{13})(\frac{17}{14}+q)\)
  12. \((p-\frac{9}{2})(\frac{10}{16}+p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{20}+b)(b-\frac{-15}{8})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{15}{8}b+\frac{4}{5}b+\frac{4}{5}.\frac{15}{8}& \text{Uitwerken } \\ & =b^2+(\frac{15}{8}+\frac{4}{5})b+\frac{60}{40} & \text{Neem samen} \\ &=b^2+\frac{107}{40}b+\frac{60}{40} & \text{Maak de som} \\ &=b^2+\frac{107}{40}b+\frac{3}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-15}{8})(x-\frac{-8}{17})& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{x}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{15}{8})} . \color{green}{(x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{17}a+\frac{15}{8}x+\frac{15}{8}.\frac{8}{17}& \text{Uitwerken } \\ & =ax+\frac{8}{17}a+\frac{15}{8}x+\frac{120}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{8}{17}a+\frac{15}{8}x+\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{20}{11}+p)(b-\frac{-4}{5})& =(\color{red}{p}+\color{orange}{\frac{20}{11}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}p+\frac{20}{11}b+\frac{20}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}p+\frac{20}{11}b+\frac{80}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{5}p+\frac{20}{11}b+\frac{16}{11} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-17}{9})(a+\frac{-14}{15})& =(\color{red}{x}+\color{orange}{\frac{17}{9}}).(\color{green}{a}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{15}x+\frac{17}{9}a-\frac{17}{9}.\frac{14}{15}& \text{Uitwerken } \\ & =ax-\frac{14}{15}x+\frac{17}{9}a-\frac{238}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{6}-a)(\frac{4}{17}+b)& =(\color{red}{-a}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{17}a-3b-3.\frac{4}{17}& \text{Uitwerken } \\ & =-ab-\frac{4}{17}a-3b-\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{19}-b)(\frac{-10}{14}+q)& =(\color{red}{-b}+\color{orange}{\frac{-7}{19}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{7}b-\frac{7}{19}q+\frac{7}{19}.\frac{5}{7}& \text{Uitwerken } \\ & =-bq+\frac{5}{7}b-\frac{7}{19}q+\frac{35}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{7}b-\frac{7}{19}q+\frac{5}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-2}{12})(b-\frac{6}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{17}p+\frac{1}{6}b-\frac{1}{6}.\frac{6}{17}& \text{Uitwerken } \\ & =bp-\frac{6}{17}p+\frac{1}{6}b-\frac{6}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{17}p+\frac{1}{6}b-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{18}+x)(p+\frac{4}{6})& =(\color{red}{x}+\color{orange}{\frac{13}{18}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{3}x+\frac{13}{18}p+\frac{13}{18}.\frac{2}{3}& \text{Uitwerken } \\ & =px+\frac{2}{3}x+\frac{13}{18}p+\frac{26}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{2}{3}x+\frac{13}{18}p+\frac{13}{27} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-14}{16})(\frac{20}{11}+x)& =(\color{red}{p}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{11}p-\frac{7}{8}x-\frac{7}{8}.\frac{20}{11}& \text{Uitwerken } \\ & =px+\frac{20}{11}p-\frac{7}{8}x-\frac{140}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{20}{11}p-\frac{7}{8}x-\frac{35}{22} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{16}+b)(\frac{-4}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{-p}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{17}b-\frac{5}{4}p-\frac{5}{4}.\frac{4}{17}& \text{Uitwerken } \\ & =-bp-\frac{4}{17}b-\frac{5}{4}p-\frac{20}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{17}b-\frac{5}{4}p-\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{6}{13})(\frac{17}{14}+q)& =(\color{red}{q}+\color{orange}{\frac{6}{13}}).(\color{green}{q}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{14}q+\frac{6}{13}q+\frac{6}{13}.\frac{17}{14}& \text{Uitwerken } \\ & =q^2+(\frac{17}{14}+\frac{6}{13})q+\frac{102}{182} & \text{Neem samen} \\ &=q^2+\frac{305}{182}q+\frac{102}{182} & \text{Maak de som} \\ &=q^2+\frac{305}{182}q+\frac{51}{91} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p-\frac{9}{2})(\frac{10}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{-9}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{8}p-\frac{9}{2}p-\frac{9}{2}.\frac{5}{8}& \text{Uitwerken } \\ & =p^2+(\frac{5}{8}+(\frac{-9}{2}))p-(\frac{-45}{16}) & \text{Neem samen} \\ &=p^2-\frac{31}{8}p-(\frac{-45}{16}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-05 13:53:26
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