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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-16}{15})(\frac{-12}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{5}q-\frac{16}{15}b+\frac{16}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =bq-\frac{4}{5}q-\frac{16}{15}b+\frac{64}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-20}{2}+x)(\frac{-7}{14}+q)& =(\color{red}{x}+\color{orange}{(-10)}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-10)} . \color{green}{(q)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}x-10q+10.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}x-10q+\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{2}x-10q+5 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-12}{9}-b)(b+\frac{9}{20})& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{9}{20}b-\frac{4}{3}b-\frac{4}{3}.\frac{9}{20}& \text{Uitwerken } \\ & =-b^2+((\frac{-9}{20})+(\frac{-4}{3}))b-\frac{36}{60} & \text{Neem samen} \\ &=-b^2-\frac{107}{60}b-\frac{36}{60} & \text{Maak de som} \\ &=-b^2-\frac{107}{60}b-\frac{3}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(q-\frac{18}{12})(\frac{18}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{18}{13}q-\frac{3}{2}a-\frac{3}{2}.\frac{18}{13}& \text{Uitwerken } \\ & =aq+\frac{18}{13}q-\frac{3}{2}a-\frac{54}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{18}{13}q-\frac{3}{2}a-\frac{27}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{4}+q)(q-\frac{-16}{10})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{5}q-\frac{5}{2}q-\frac{5}{2}.\frac{8}{5}& \text{Uitwerken } \\ & =q^2+(\frac{8}{5}+(\frac{-5}{2}))q-(\frac{-40}{10}) & \text{Neem samen} \\ &=q^2-\frac{9}{10}q-(\frac{-40}{10}) & \text{Maak de som} \\ &=q^2-\frac{9}{10}q+4 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(b-(-13))(\frac{-18}{20}+a)& =(\color{red}{b}+\color{orange}{13}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(13)} . \color{green}{(a)} + \color{orange}{(13)} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{10}b+13a-13.\frac{9}{10}& \text{Uitwerken } \\ & =ab-\frac{9}{10}b+13a-\frac{117}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{18}-a)(q+\frac{-13}{16})& =(\color{red}{-a}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{13}{16}a+\frac{1}{6}q-\frac{1}{6}.\frac{13}{16}& \text{Uitwerken } \\ & =-aq+\frac{13}{16}a+\frac{1}{6}q-\frac{13}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{7}-x)((-10)+b)& =(\color{red}{-x}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(-10)} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -bx+10x+\frac{1}{7}b-\frac{1}{7}.10& \text{Uitwerken } \\ & =-bx+10x+\frac{1}{7}b-\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-15)-b)(p-\frac{2}{20})& =(\color{red}{-b}+\color{orange}{(-15)}).(\color{green}{p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(-15)} . \color{green}{(p)} + \color{orange}{(-15)} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{10}b-15p+15.\frac{1}{10}& \text{Uitwerken } \\ & =-bp+\frac{1}{10}b-15p+\frac{15}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{10}b-15p+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{4}-p)(\frac{19}{9}-a)& =(\color{red}{-p}+\color{orange}{\frac{3}{2}}).(\color{green}{-a}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}p-\frac{3}{2}a+\frac{3}{2}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}p-\frac{3}{2}a+\frac{57}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{9}p-\frac{3}{2}a+\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{14}+p)(\frac{9}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{13}{14}}).(\color{green}{-x}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{13}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{17}p-\frac{13}{14}x+\frac{13}{14}.\frac{9}{17}& \text{Uitwerken } \\ & =-px+\frac{9}{17}p-\frac{13}{14}x+\frac{117}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-19}{3}+a)(a-\frac{-15}{6})& =(\color{red}{a}+\color{orange}{\frac{-19}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{2}a-\frac{19}{3}a-\frac{19}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =a^2+(\frac{5}{2}+(\frac{-19}{3}))a-(\frac{-95}{6}) & \text{Neem samen} \\ &=a^2-\frac{23}{6}a-(\frac{-95}{6}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-30 03:12:37
Een site van Busleyden Atheneum Mechelen