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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{16}{2})(\frac{-20}{5}+a)& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4q-8a+8.4& \text{Uitwerken } \\ & =aq-4q-8a+32 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{9}+q)(\frac{13}{9}-p)& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{-p}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{9}q-\frac{7}{9}p+\frac{7}{9}.\frac{13}{9}& \text{Uitwerken } \\ & =-pq+\frac{13}{9}q-\frac{7}{9}p+\frac{91}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-10}{5})(a-\frac{-16}{17})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{17}a-2a-2.\frac{16}{17}& \text{Uitwerken } \\ & =a^2+(\frac{16}{17}+(-2))a-(\frac{-32}{17}) & \text{Neem samen} \\ &=a^2-\frac{18}{17}a-(\frac{-32}{17}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-18}{19})(\frac{11}{13}+q)& =(\color{red}{x}+\color{orange}{\frac{18}{19}}).(\color{green}{q}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{13}x+\frac{18}{19}q+\frac{18}{19}.\frac{11}{13}& \text{Uitwerken } \\ & =qx+\frac{11}{13}x+\frac{18}{19}q+\frac{198}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{4}{15})(a+\frac{-18}{3})& =(\color{red}{b}+\color{orange}{\frac{4}{15}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{4}{15})} . \color{green}{(a)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6b+\frac{4}{15}a-\frac{4}{15}.6& \text{Uitwerken } \\ & =ab-6b+\frac{4}{15}a-\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-6b+\frac{4}{15}a-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-16}{15})(\frac{12}{8}+b)& =(\color{red}{q}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{2}q-\frac{16}{15}b-\frac{16}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =bq+\frac{3}{2}q-\frac{16}{15}b-\frac{48}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{2}q-\frac{16}{15}b-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{5}-b)(a-\frac{-6}{17})& =(\color{red}{-b}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{6}{17}b-\frac{8}{5}a-\frac{8}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =-ab-\frac{6}{17}b-\frac{8}{5}a-\frac{48}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-5}{15})(\frac{9}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{-q}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{11}a-\frac{1}{3}q+\frac{1}{3}.\frac{9}{11}& \text{Uitwerken } \\ & =-aq+\frac{9}{11}a-\frac{1}{3}q+\frac{9}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{11}a-\frac{1}{3}q+\frac{3}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-5}{10})(\frac{7}{17}+p)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{17}a-\frac{1}{2}p-\frac{1}{2}.\frac{7}{17}& \text{Uitwerken } \\ & =ap+\frac{7}{17}a-\frac{1}{2}p-\frac{7}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{9}+q)(a-\frac{-3}{4})& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{4}q+\frac{5}{3}a+\frac{5}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =aq+\frac{3}{4}q+\frac{5}{3}a+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{4}q+\frac{5}{3}a+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-17}{4})(b-\frac{-20}{8})& =(\color{red}{b}+\color{orange}{\frac{17}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{2}b+\frac{17}{4}b+\frac{17}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =b^2+(\frac{5}{2}+\frac{17}{4})b+\frac{85}{8} & \text{Neem samen} \\ &=b^2+\frac{27}{4}b+\frac{85}{8} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{19}-x)(a+\frac{-4}{4})& =(\color{red}{-x}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x+\frac{11}{19}a-\frac{11}{19}.1& \text{Uitwerken } \\ & =-ax+1x+\frac{11}{19}a-\frac{11}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-10 07:33:42
Een site van Busleyden Atheneum Mechelen