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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(12+q)(q-\frac{-4}{19})& =(\color{red}{q}+\color{orange}{12}).(\color{green}{q}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(12)} . \color{green}{(q)} + \color{orange}{(12)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{4}{19}q+12q+12.\frac{4}{19}& \text{Uitwerken } \\ & =q^2+(\frac{4}{19}+12)q+\frac{48}{19} & \text{Neem samen} \\ &=q^2+\frac{232}{19}q+\frac{48}{19} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-2}{13})(\frac{-8}{16}+x)& =(\color{red}{q}+\color{orange}{\frac{2}{13}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q+\frac{2}{13}x-\frac{2}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q+\frac{2}{13}x-\frac{2}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{2}q+\frac{2}{13}x-\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{4}+a)(p+\frac{-5}{12})& =(\color{red}{a}+\color{orange}{\frac{17}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{17}{4})} . \color{green}{(p)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{12}a+\frac{17}{4}p-\frac{17}{4}.\frac{5}{12}& \text{Uitwerken } \\ & =ap-\frac{5}{12}a+\frac{17}{4}p-\frac{85}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{16}{4})(x+\frac{-15}{2})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{15}{2}x-4x+4.\frac{15}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-15}{2})+(-4))x+\frac{60}{2} & \text{Neem samen} \\ &=x^2-\frac{23}{2}x+\frac{60}{2} & \text{Maak de som} \\ &=x^2-\frac{23}{2}x+30 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b+\frac{16}{6})(\frac{2}{3}-b)& =(\color{red}{b}+\color{orange}{\frac{8}{3}}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{3}b-\frac{8}{3}b+\frac{8}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{3}+(\frac{-8}{3}))b+(\frac{-16}{9}) & \text{Neem samen} \\ &=-b^2-\frac{6}{3}b+(\frac{-16}{9}) & \text{Maak de som} \\ &=-b^2-2b+(\frac{-16}{9}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{9}{20}+b)(\frac{4}{11}+p)& =(\color{red}{b}+\color{orange}{\frac{9}{20}}).(\color{green}{p}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{11}b+\frac{9}{20}p+\frac{9}{20}.\frac{4}{11}& \text{Uitwerken } \\ & =bp+\frac{4}{11}b+\frac{9}{20}p+\frac{36}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{11}b+\frac{9}{20}p+\frac{9}{55} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{17}+a)(q-\frac{-20}{16})& =(\color{red}{a}+\color{orange}{\frac{-14}{17}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{4}a-\frac{14}{17}q-\frac{14}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =aq+\frac{5}{4}a-\frac{14}{17}q-\frac{70}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{4}a-\frac{14}{17}q-\frac{35}{34} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{4}{13})(\frac{-15}{12}+p)& =(\color{red}{b}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{4}b-\frac{4}{13}p+\frac{4}{13}.\frac{5}{4}& \text{Uitwerken } \\ & =bp-\frac{5}{4}b-\frac{4}{13}p+\frac{20}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{4}b-\frac{4}{13}p+\frac{5}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-8}{12})(\frac{8}{5}+q)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{5}b+\frac{2}{3}q+\frac{2}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =bq+\frac{8}{5}b+\frac{2}{3}q+\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{13}{20})(b-\frac{-12}{9})& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{3}x-\frac{13}{20}b-\frac{13}{20}.\frac{4}{3}& \text{Uitwerken } \\ & =bx+\frac{4}{3}x-\frac{13}{20}b-\frac{52}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{3}x-\frac{13}{20}b-\frac{13}{15} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{5}+a)(\frac{-12}{10}+a)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{6}{5}a+4a-4.\frac{6}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-6}{5})+4)a-(\frac{-24}{5}) & \text{Neem samen} \\ &=a^2+\frac{14}{5}a-(\frac{-24}{5}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b-\frac{16}{8})((-9)-q)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bq-9b+2q+2.9& \text{Uitwerken } \\ & =-bq-9b+2q+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-05 21:52:32
Een site van Busleyden Atheneum Mechelen