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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{6}{6})(\frac{19}{17}+p)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{17}b+1p+1.\frac{19}{17}& \text{Uitwerken } \\ & =bp+\frac{19}{17}b+1p+\frac{19}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{9}{14})(b-\frac{7}{18})& =(\color{red}{x}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{18}x-\frac{9}{14}b+\frac{9}{14}.\frac{7}{18}& \text{Uitwerken } \\ & =bx-\frac{7}{18}x-\frac{9}{14}b+\frac{63}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{18}x-\frac{9}{14}b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{2}{4})(\frac{-20}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{7}p+\frac{1}{2}a-\frac{1}{2}.\frac{20}{7}& \text{Uitwerken } \\ & =ap-\frac{20}{7}p+\frac{1}{2}a-\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{20}{7}p+\frac{1}{2}a-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{6}{19}+b)(\frac{-12}{15}-b)& =(\color{red}{b}+\color{orange}{\frac{6}{19}}).(\color{green}{-b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{6}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{5}b-\frac{6}{19}b-\frac{6}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{5})+(\frac{-6}{19}))b-\frac{24}{95} & \text{Neem samen} \\ &=-b^2-\frac{106}{95}b-\frac{24}{95} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-8}{10})(\frac{-5}{19}-x)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{19}b-\frac{4}{5}x-\frac{4}{5}.\frac{5}{19}& \text{Uitwerken } \\ & =-bx-\frac{5}{19}b-\frac{4}{5}x-\frac{20}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{19}b-\frac{4}{5}x-\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{8}{18})(\frac{-8}{6}+p)& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{3}x+\frac{4}{9}p-\frac{4}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =px-\frac{4}{3}x+\frac{4}{9}p-\frac{16}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-9}{13})(\frac{-14}{15}-q)& =(\color{red}{a}+\color{orange}{\frac{9}{13}}).(\color{green}{-q}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{9}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{14}{15}a-\frac{9}{13}q-\frac{9}{13}.\frac{14}{15}& \text{Uitwerken } \\ & =-aq-\frac{14}{15}a-\frac{9}{13}q-\frac{126}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{14}{15}a-\frac{9}{13}q-\frac{42}{65} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{5}+x)(\frac{4}{5}+b)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{5}x+2b+2.\frac{4}{5}& \text{Uitwerken } \\ & =bx+\frac{4}{5}x+2b+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-14}{17})(\frac{-3}{2}+b)& =(\color{red}{b}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{2}b-\frac{14}{17}b+\frac{14}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{2})+(\frac{-14}{17}))b+\frac{42}{34} & \text{Neem samen} \\ &=b^2-\frac{79}{34}b+\frac{42}{34} & \text{Maak de som} \\ &=b^2-\frac{79}{34}b+\frac{21}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-17}{20})(p-\frac{-16}{7})& =(\color{red}{p}+\color{orange}{\frac{17}{20}}).(\color{green}{p}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{17}{20})} . \color{green}{(p)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{16}{7}p+\frac{17}{20}p+\frac{17}{20}.\frac{16}{7}& \text{Uitwerken } \\ & =p^2+(\frac{16}{7}+\frac{17}{20})p+\frac{272}{140} & \text{Neem samen} \\ &=p^2+\frac{439}{140}p+\frac{272}{140} & \text{Maak de som} \\ &=p^2+\frac{439}{140}p+\frac{68}{35} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{14}{9}-p)(\frac{-17}{5}+q)& =(\color{red}{-p}+\color{orange}{\frac{14}{9}}).(\color{green}{q}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{14}{9})} . \color{green}{(q)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{5}p+\frac{14}{9}q-\frac{14}{9}.\frac{17}{5}& \text{Uitwerken } \\ & =-pq+\frac{17}{5}p+\frac{14}{9}q-\frac{238}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-3}{8})(16+q)& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{16})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(16)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = qx+16x-\frac{3}{8}q-\frac{3}{8}.16& \text{Uitwerken } \\ & =qx+16x-\frac{3}{8}q-\frac{48}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+16x-\frac{3}{8}q-6 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-22 12:08:11
Een site van Busleyden Atheneum Mechelen