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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{12}-x)(b-\frac{-10}{8})& =(\color{red}{-x}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{4}x-\frac{5}{3}b-\frac{5}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =-bx-\frac{5}{4}x-\frac{5}{3}b-\frac{25}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+(-10))(q-\frac{10}{4})& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{2}b-10q+10.\frac{5}{2}& \text{Uitwerken } \\ & =bq-\frac{5}{2}b-10q+\frac{50}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{2}b-10q+25 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-(-15))(b-\frac{-5}{17})& =(\color{red}{b}+\color{orange}{15}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(15)} . \color{green}{(b)} + \color{orange}{(15)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{17}b+15b+15.\frac{5}{17}& \text{Uitwerken } \\ & =b^2+(\frac{5}{17}+15)b+\frac{75}{17} & \text{Neem samen} \\ &=b^2+\frac{260}{17}b+\frac{75}{17} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p-\frac{10}{19})(b-\frac{-6}{14})& =(\color{red}{p}+\color{orange}{\frac{-10}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{7}p-\frac{10}{19}b-\frac{10}{19}.\frac{3}{7}& \text{Uitwerken } \\ & =bp+\frac{3}{7}p-\frac{10}{19}b-\frac{30}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{13}+p)(x+\frac{-14}{19})& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{19}p-\frac{2}{13}x+\frac{2}{13}.\frac{14}{19}& \text{Uitwerken } \\ & =px-\frac{14}{19}p-\frac{2}{13}x+\frac{28}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-5}{20})(\frac{-11}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{4}b+\frac{1}{4}p-\frac{1}{4}.\frac{11}{4}& \text{Uitwerken } \\ & =bp-\frac{11}{4}b+\frac{1}{4}p-\frac{11}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-13}{8})(q+\frac{-20}{9})& =(\color{red}{q}+\color{orange}{\frac{13}{8}}).(\color{green}{q}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{20}{9}q+\frac{13}{8}q-\frac{13}{8}.\frac{20}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-20}{9})+\frac{13}{8})q-(\frac{-260}{72}) & \text{Neem samen} \\ &=q^2-\frac{43}{72}q-(\frac{-260}{72}) & \text{Maak de som} \\ &=q^2-\frac{43}{72}q+\frac{65}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{3}-x)(\frac{-13}{9}+x)& =(\color{red}{-x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{9}x+2x-2.\frac{13}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{9}+2)x-\frac{26}{9} & \text{Neem samen} \\ &=-x^2+\frac{31}{9}x-\frac{26}{9} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{1}{19}-p)(\frac{10}{8}+x)& =(\color{red}{-p}+\color{orange}{\frac{1}{19}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{4}p+\frac{1}{19}x+\frac{1}{19}.\frac{5}{4}& \text{Uitwerken } \\ & =-px-\frac{5}{4}p+\frac{1}{19}x+\frac{5}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-2}{12})(a-\frac{-14}{5})& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{5}p-\frac{1}{6}a-\frac{1}{6}.\frac{14}{5}& \text{Uitwerken } \\ & =ap+\frac{14}{5}p-\frac{1}{6}a-\frac{14}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{14}{5}p-\frac{1}{6}a-\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-7}{16})(\frac{-12}{14}+q)& =(\color{red}{p}+\color{orange}{\frac{-7}{16}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{7}p-\frac{7}{16}q+\frac{7}{16}.\frac{6}{7}& \text{Uitwerken } \\ & =pq-\frac{6}{7}p-\frac{7}{16}q+\frac{42}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{7}p-\frac{7}{16}q+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{8}+p)(\frac{-20}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{-15}{8}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ap-5p-\frac{15}{8}a+\frac{15}{8}.5& \text{Uitwerken } \\ & =ap-5p-\frac{15}{8}a+\frac{75}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-22 20:18:22
Een site van Busleyden Atheneum Mechelen