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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-10}{18}-b)(\frac{9}{5}+a)& =(\color{red}{-b}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{5}b-\frac{5}{9}a-\frac{5}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =-ab-\frac{9}{5}b-\frac{5}{9}a-\frac{45}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{9}{5}b-\frac{5}{9}a-1 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{19}-x)(\frac{-8}{20}-q)& =(\color{red}{-x}+\color{orange}{\frac{20}{19}}).(\color{green}{-q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{20}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{5}x-\frac{20}{19}q-\frac{20}{19}.\frac{2}{5}& \text{Uitwerken } \\ & =qx+\frac{2}{5}x-\frac{20}{19}q-\frac{40}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{5}x-\frac{20}{19}q-\frac{8}{19} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{2}+x)(\frac{-14}{10}-a)& =(\color{red}{x}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{5}x-5a-5.\frac{7}{5}& \text{Uitwerken } \\ & =-ax-\frac{7}{5}x-5a-\frac{35}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{5}x-5a-7 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{19}{15}-p)(\frac{-18}{6}+p)& =(\color{red}{-p}+\color{orange}{\frac{19}{15}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-3)} + \color{orange}{(\frac{19}{15})} . \color{green}{(p)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -pp+3p+\frac{19}{15}p-\frac{19}{15}.3& \text{Uitwerken } \\ & =-p^2+(3+\frac{19}{15})p-\frac{57}{15} & \text{Neem samen} \\ &=-p^2+\frac{64}{15}p-\frac{57}{15} & \text{Maak de som} \\ &=-p^2+\frac{64}{15}p-\frac{19}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{20}+b)(\frac{14}{8}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{4}b-\frac{1}{2}p+\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =-bp+\frac{7}{4}b-\frac{1}{2}p+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{18}{14})(x-\frac{19}{7})& =(\color{red}{x}+\color{orange}{\frac{-9}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{7}x-\frac{9}{7}x+\frac{9}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{7})+(\frac{-9}{7}))x+\frac{171}{49} & \text{Neem samen} \\ &=x^2-\frac{28}{7}x+\frac{171}{49} & \text{Maak de som} \\ &=x^2-4x+\frac{171}{49} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(x-\frac{5}{8})(a+\frac{-6}{16})& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{a}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{8}x-\frac{5}{8}a+\frac{5}{8}.\frac{3}{8}& \text{Uitwerken } \\ & =ax-\frac{3}{8}x-\frac{5}{8}a+\frac{15}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{7}+p)(\frac{-1}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{17}{7}}).(\color{green}{-p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{17}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{6}p-\frac{17}{7}p-\frac{17}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{6})+(\frac{-17}{7}))p-\frac{17}{42} & \text{Neem samen} \\ &=-p^2-\frac{109}{42}p-\frac{17}{42} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{9}-p)(b-\frac{-11}{15})& =(\color{red}{-p}+\color{orange}{\frac{20}{9}}).(\color{green}{b}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{15}p+\frac{20}{9}b+\frac{20}{9}.\frac{11}{15}& \text{Uitwerken } \\ & =-bp-\frac{11}{15}p+\frac{20}{9}b+\frac{220}{135} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{15}p+\frac{20}{9}b+\frac{44}{27} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-12}{3})(a-\frac{-2}{2})& =(\color{red}{a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a+4a+4.1& \text{Uitwerken } \\ & =a^2+(1+4)a+4 & \text{Neem samen} \\ &=a^2+5a+4 & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{16}{2}+p)(\frac{2}{14}+x)& =(\color{red}{p}+\color{orange}{8}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(8)} . \color{green}{(x)} + \color{orange}{(8)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{7}p+8x+8.\frac{1}{7}& \text{Uitwerken } \\ & =px+\frac{1}{7}p+8x+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{16}{16})(\frac{-11}{14}-q)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{14}p+1q+1.\frac{11}{14}& \text{Uitwerken } \\ & =-pq-\frac{11}{14}p+1q+\frac{11}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-28 06:28:45
Een site van Busleyden Atheneum Mechelen