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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-18}{10})(b+\frac{17}{4})& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{4}a-\frac{9}{5}b-\frac{9}{5}.\frac{17}{4}& \text{Uitwerken } \\ & =ab+\frac{17}{4}a-\frac{9}{5}b-\frac{153}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{4}+p)(\frac{-1}{4}-q)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{4}p-2q-2.\frac{1}{4}& \text{Uitwerken } \\ & =-pq-\frac{1}{4}p-2q-\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{4}p-2q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{18}+b)(\frac{2}{14}+b)& =(\color{red}{b}+\color{orange}{\frac{-7}{18}}).(\color{green}{b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{7}b-\frac{7}{18}b-\frac{7}{18}.\frac{1}{7}& \text{Uitwerken } \\ & =b^2+(\frac{1}{7}+(\frac{-7}{18}))b-(\frac{-7}{126}) & \text{Neem samen} \\ &=b^2-\frac{31}{126}b-(\frac{-7}{126}) & \text{Maak de som} \\ &=b^2-\frac{31}{126}b+\frac{1}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(q+\frac{4}{2})(\frac{-19}{10}+x)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{10}q+2x-2.\frac{19}{10}& \text{Uitwerken } \\ & =qx-\frac{19}{10}q+2x-\frac{38}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{10}q+2x-\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{9}-a)(\frac{18}{5}-p)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{5}a+1p-1.\frac{18}{5}& \text{Uitwerken } \\ & =ap-\frac{18}{5}a+1p-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{15}+a)(q-\frac{-19}{9})& =(\color{red}{a}+\color{orange}{\frac{7}{15}}).(\color{green}{q}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{9}a+\frac{7}{15}q+\frac{7}{15}.\frac{19}{9}& \text{Uitwerken } \\ & =aq+\frac{19}{9}a+\frac{7}{15}q+\frac{133}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{19}-a)(a+\frac{-9}{8})& =(\color{red}{-a}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{8}a-\frac{14}{19}a+\frac{14}{19}.\frac{9}{8}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{8}+(\frac{-14}{19}))a+(\frac{-126}{152}) & \text{Neem samen} \\ &=-a^2+\frac{59}{152}a+(\frac{-126}{152}) & \text{Maak de som} \\ &=-a^2+\frac{59}{152}a+(\frac{-63}{76}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-2}{16}+b)(p+\frac{-4}{19})& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{19}b-\frac{1}{8}p+\frac{1}{8}.\frac{4}{19}& \text{Uitwerken } \\ & =bp-\frac{4}{19}b-\frac{1}{8}p+\frac{4}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{19}b-\frac{1}{8}p+\frac{1}{38} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{3}-q)(\frac{-1}{7}-q)& =(\color{red}{-q}+\color{orange}{\frac{-19}{3}}).(\color{green}{-q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{7}q+\frac{19}{3}q+\frac{19}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =q^2+(\frac{1}{7}+\frac{19}{3})q+\frac{19}{21} & \text{Neem samen} \\ &=q^2+\frac{136}{21}q+\frac{19}{21} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{13}+p)(\frac{-8}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{8}{5}p+\frac{18}{13}p-\frac{18}{13}.\frac{8}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-8}{5})+\frac{18}{13})p-(\frac{-144}{65}) & \text{Neem samen} \\ &=p^2-\frac{14}{65}p-(\frac{-144}{65}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{15}+a)(\frac{-20}{11}-a)& =(\color{red}{a}+\color{orange}{\frac{-2}{15}}).(\color{green}{-a}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{11}a+\frac{2}{15}a+\frac{2}{15}.\frac{20}{11}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{11})+\frac{2}{15})a+(\frac{-40}{165}) & \text{Neem samen} \\ &=-a^2-\frac{278}{165}a+(\frac{-40}{165}) & \text{Maak de som} \\ &=-a^2-\frac{278}{165}a+(\frac{-8}{33}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}((-16)-p)(x-\frac{14}{9})& =(\color{red}{-p}+\color{orange}{(-16)}).(\color{green}{x}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(-16)} . \color{green}{(x)} + \color{orange}{(-16)} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{14}{9}p-16x+16.\frac{14}{9}& \text{Uitwerken } \\ & =-px+\frac{14}{9}p-16x+\frac{224}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-07 20:44:23
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