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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-14}{14})(\frac{18}{17}-a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{18}{17}a-1a+1.\frac{18}{17}& \text{Uitwerken } \\ & =-a^2+(\frac{18}{17}+(-1))a+(\frac{-18}{17}) & \text{Neem samen} \\ &=-a^2+\frac{1}{17}a+(\frac{-18}{17}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q-\frac{13}{11})(\frac{-3}{4}-b)& =(\color{red}{q}+\color{orange}{\frac{-13}{11}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{4}q+\frac{13}{11}b+\frac{13}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq-\frac{3}{4}q+\frac{13}{11}b+\frac{39}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{9}-p)(p-\frac{16}{3})& =(\color{red}{-p}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{16}{3}p-\frac{8}{9}p+\frac{8}{9}.\frac{16}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{16}{3}+(\frac{-8}{9}))p+(\frac{-128}{27}) & \text{Neem samen} \\ &=-p^2+\frac{40}{9}p+(\frac{-128}{27}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-7}{5})(b-\frac{-12}{6})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b-\frac{7}{5}b-\frac{7}{5}.2& \text{Uitwerken } \\ & =b^2+(2+(\frac{-7}{5}))b-(\frac{-14}{5}) & \text{Neem samen} \\ &=b^2+\frac{3}{5}b-(\frac{-14}{5}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{20}{20})(p-\frac{13}{19})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{19}a-1p+1.\frac{13}{19}& \text{Uitwerken } \\ & =ap-\frac{13}{19}a-1p+\frac{13}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{8}{17})(\frac{-2}{15}-q)& =(\color{red}{p}+\color{orange}{\frac{8}{17}}).(\color{green}{-q}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{8}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{15}p-\frac{8}{17}q-\frac{8}{17}.\frac{2}{15}& \text{Uitwerken } \\ & =-pq-\frac{2}{15}p-\frac{8}{17}q-\frac{16}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{18}{15})(\frac{18}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{5}a-\frac{6}{5}b-\frac{6}{5}.\frac{9}{5}& \text{Uitwerken } \\ & =ab+\frac{9}{5}a-\frac{6}{5}b-\frac{54}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{13}+q)(b-\frac{7}{13})& =(\color{red}{q}+\color{orange}{\frac{4}{13}}).(\color{green}{b}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{13}q+\frac{4}{13}b-\frac{4}{13}.\frac{7}{13}& \text{Uitwerken } \\ & =bq-\frac{7}{13}q+\frac{4}{13}b-\frac{28}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{5}+a)(a+\frac{-16}{14})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{7}a+\frac{6}{5}a-\frac{6}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{7})+\frac{6}{5})a-(\frac{-48}{35}) & \text{Neem samen} \\ &=a^2+\frac{2}{35}a-(\frac{-48}{35}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{1}{17})(b+\frac{15}{10})& =(\color{red}{b}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{2}b-\frac{1}{17}b-\frac{1}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+(\frac{3}{2}+(\frac{-1}{17}))b-(\frac{-3}{34}) & \text{Neem samen} \\ &=b^2+\frac{49}{34}b-(\frac{-3}{34}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-10}{3})(\frac{-8}{5}+x)& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{5}q+\frac{10}{3}x-\frac{10}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =qx-\frac{8}{5}q+\frac{10}{3}x-\frac{80}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{8}{5}q+\frac{10}{3}x-\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-1}{20}+q)(x+\frac{-20}{7})& =(\color{red}{q}+\color{orange}{\frac{-1}{20}}).(\color{green}{x}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{20}{7}q-\frac{1}{20}x+\frac{1}{20}.\frac{20}{7}& \text{Uitwerken } \\ & =qx-\frac{20}{7}q-\frac{1}{20}x+\frac{20}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{20}{7}q-\frac{1}{20}x+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-20 10:29:18
Een site van Busleyden Atheneum Mechelen