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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{15}-a)(b-\frac{16}{16})& =(\color{red}{-a}+\color{orange}{\frac{19}{15}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1a+\frac{19}{15}b-\frac{19}{15}.1& \text{Uitwerken } \\ & =-ab+1a+\frac{19}{15}b-\frac{19}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{11}-a)(b+\frac{20}{3})& =(\color{red}{-a}+\color{orange}{\frac{-4}{11}}).(\color{green}{b}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{20}{3}a-\frac{4}{11}b-\frac{4}{11}.\frac{20}{3}& \text{Uitwerken } \\ & =-ab-\frac{20}{3}a-\frac{4}{11}b-\frac{80}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{17}{2})(\frac{-15}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{-17}{2}}).(\color{green}{-q}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{13}x+\frac{17}{2}q+\frac{17}{2}.\frac{15}{13}& \text{Uitwerken } \\ & =-qx-\frac{15}{13}x+\frac{17}{2}q+\frac{255}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{16}{7})(q+14)& =(\color{red}{b}+\color{orange}{\frac{-16}{7}}).(\color{green}{q}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(14)} + \color{orange}{(\frac{-16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = bq+14b-\frac{16}{7}q-\frac{16}{7}.14& \text{Uitwerken } \\ & =bq+14b-\frac{16}{7}q-\frac{224}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+14b-\frac{16}{7}q-32 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{11}{3})(b+3)& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bb+3b+\frac{11}{3}b+\frac{11}{3}.3& \text{Uitwerken } \\ & =b^2+(3+\frac{11}{3})b+\frac{33}{3} & \text{Neem samen} \\ &=b^2+\frac{20}{3}b+\frac{33}{3} & \text{Maak de som} \\ &=b^2+\frac{20}{3}b+11 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{7}+a)(\frac{10}{14}+q)& =(\color{red}{a}+\color{orange}{\frac{18}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{18}{7})} . \color{green}{(q)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{7}a+\frac{18}{7}q+\frac{18}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =aq+\frac{5}{7}a+\frac{18}{7}q+\frac{90}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{11}+q)(q+\frac{2}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{11}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{5}q+\frac{1}{11}q+\frac{1}{11}.\frac{1}{5}& \text{Uitwerken } \\ & =q^2+(\frac{1}{5}+\frac{1}{11})q+\frac{1}{55} & \text{Neem samen} \\ &=q^2+\frac{16}{55}q+\frac{1}{55} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{5}+x)(p+\frac{-18}{17})& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{18}{17}x+\frac{4}{5}p-\frac{4}{5}.\frac{18}{17}& \text{Uitwerken } \\ & =px-\frac{18}{17}x+\frac{4}{5}p-\frac{72}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-5}{14})(\frac{4}{4}+p)& =(\color{red}{q}+\color{orange}{\frac{5}{14}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q+\frac{5}{14}p+\frac{5}{14}.1& \text{Uitwerken } \\ & =pq+1q+\frac{5}{14}p+\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{2}{19}+b)(\frac{2}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{19}}).(\color{green}{-b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{2}{9}b-\frac{2}{19}b+\frac{2}{19}.\frac{2}{9}& \text{Uitwerken } \\ & =-b^2+(\frac{2}{9}+(\frac{-2}{19}))b+(\frac{-4}{171}) & \text{Neem samen} \\ &=-b^2+\frac{20}{171}b+(\frac{-4}{171}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{5}+a)(\frac{-2}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{-14}{5}}).(\color{green}{-x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{7}a+\frac{14}{5}x+\frac{14}{5}.\frac{2}{7}& \text{Uitwerken } \\ & =-ax-\frac{2}{7}a+\frac{14}{5}x+\frac{28}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{2}{7}a+\frac{14}{5}x+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{16}{8})(p+\frac{-16}{8})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2x-2p+2.2& \text{Uitwerken } \\ & =px-2x-2p+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-12 23:09:18
Een site van Busleyden Atheneum Mechelen