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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{5}+p)(\frac{-7}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{4}p+\frac{3}{5}p-\frac{3}{5}.\frac{7}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{4})+\frac{3}{5})p-(\frac{-21}{20}) & \text{Neem samen} \\ &=p^2-\frac{23}{20}p-(\frac{-21}{20}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{3}-x)(b+\frac{10}{18})& =(\color{red}{-x}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{9}x+\frac{4}{3}b+\frac{4}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =-bx-\frac{5}{9}x+\frac{4}{3}b+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-19}{7})((-9)+p)& =(\color{red}{p}+\color{orange}{\frac{19}{7}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-9)} + \color{orange}{(\frac{19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = pp-9p+\frac{19}{7}p-\frac{19}{7}.9& \text{Uitwerken } \\ & =p^2+((-9)+\frac{19}{7})p-(\frac{-171}{7}) & \text{Neem samen} \\ &=p^2-\frac{44}{7}p-(\frac{-171}{7}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{-3}{4})(b-\frac{19}{2})& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{2}a-\frac{3}{4}b+\frac{3}{4}.\frac{19}{2}& \text{Uitwerken } \\ & =ab-\frac{19}{2}a-\frac{3}{4}b+\frac{57}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-16}{18})(a+\frac{12}{7})& =(\color{red}{p}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{12}{7}p-\frac{8}{9}a-\frac{8}{9}.\frac{12}{7}& \text{Uitwerken } \\ & =ap+\frac{12}{7}p-\frac{8}{9}a-\frac{96}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{12}{7}p-\frac{8}{9}a-\frac{32}{21} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-16}{16}-p)(x-(-19))& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(19)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = -px-19p-1x-1.19& \text{Uitwerken } \\ & =-px-19p-1x-19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(18-b)(x+\frac{20}{8})& =(\color{red}{-b}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{2}b+18x+18.\frac{5}{2}& \text{Uitwerken } \\ & =-bx-\frac{5}{2}b+18x+\frac{90}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{2}b+18x+45 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-10}{3})(a-\frac{7}{20})& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{20}x+\frac{10}{3}a-\frac{10}{3}.\frac{7}{20}& \text{Uitwerken } \\ & =ax-\frac{7}{20}x+\frac{10}{3}a-\frac{70}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{20}x+\frac{10}{3}a-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{4}-a)(a-\frac{-17}{20})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{20}a+\frac{3}{2}a+\frac{3}{2}.\frac{17}{20}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{20})+\frac{3}{2})a+(\frac{-51}{40}) & \text{Neem samen} \\ &=-a^2+\frac{13}{20}a+(\frac{-51}{40}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q+18)(\frac{-15}{9}-q)& =(\color{red}{q}+\color{orange}{18}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(18)} . \color{green}{(-q)} + \color{orange}{(18)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{5}{3}q-18q-18.\frac{5}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-5}{3})+(-18))q-\frac{90}{3} & \text{Neem samen} \\ &=-q^2-\frac{59}{3}q-\frac{90}{3} & \text{Maak de som} \\ &=-q^2-\frac{59}{3}q-30 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(q-\frac{16}{14})(\frac{18}{9}+q)& =(\color{red}{q}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq+2q-\frac{8}{7}q-\frac{8}{7}.2& \text{Uitwerken } \\ & =q^2+(2+(\frac{-8}{7}))q-(\frac{-16}{7}) & \text{Neem samen} \\ &=q^2+\frac{6}{7}q-(\frac{-16}{7}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-12}{17})(\frac{-2}{8}+q)& =(\color{red}{p}+\color{orange}{\frac{-12}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}p-\frac{12}{17}q+\frac{12}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}p-\frac{12}{17}q+\frac{12}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{4}p-\frac{12}{17}q+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-15 02:08:49
Een site van Busleyden Atheneum Mechelen