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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{15}-p)(q-\frac{-9}{10})& =(\color{red}{-p}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{10}p-\frac{16}{15}q-\frac{16}{15}.\frac{9}{10}& \text{Uitwerken } \\ & =-pq-\frac{9}{10}p-\frac{16}{15}q-\frac{144}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{9}{10}p-\frac{16}{15}q-\frac{24}{25} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{9}{3}-b)(x-\frac{7}{15})& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{15}b+3x-3.\frac{7}{15}& \text{Uitwerken } \\ & =-bx+\frac{7}{15}b+3x-\frac{21}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{7}{15}b+3x-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-13}{8})(\frac{-9}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-13}{8}}).(\color{green}{q}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{17}a-\frac{13}{8}q+\frac{13}{8}.\frac{9}{17}& \text{Uitwerken } \\ & =aq-\frac{9}{17}a-\frac{13}{8}q+\frac{117}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{17}{5})(p-\frac{3}{19})& =(\color{red}{b}+\color{orange}{\frac{17}{5}}).(\color{green}{p}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{17}{5})} . \color{green}{(p)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{19}b+\frac{17}{5}p-\frac{17}{5}.\frac{3}{19}& \text{Uitwerken } \\ & =bp-\frac{3}{19}b+\frac{17}{5}p-\frac{51}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{6}{17})(p-\frac{-10}{20})& =(\color{red}{x}+\color{orange}{\frac{6}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{6}{17})} . \color{green}{(p)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{2}x+\frac{6}{17}p+\frac{6}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =px+\frac{1}{2}x+\frac{6}{17}p+\frac{6}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{2}x+\frac{6}{17}p+\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{6}{18})(\frac{12}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bb+3b-\frac{1}{3}b+\frac{1}{3}.3& \text{Uitwerken } \\ & =-b^2+(3+(\frac{-1}{3}))b+(\frac{-3}{3}) & \text{Neem samen} \\ &=-b^2+\frac{8}{3}b+(\frac{-3}{3}) & \text{Maak de som} \\ &=-b^2+\frac{8}{3}b+(-1) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{13}-b)(\frac{-16}{9}-a)& =(\color{red}{-b}+\color{orange}{\frac{5}{13}}).(\color{green}{-a}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{5}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{16}{9}b-\frac{5}{13}a-\frac{5}{13}.\frac{16}{9}& \text{Uitwerken } \\ & =ab+\frac{16}{9}b-\frac{5}{13}a-\frac{80}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{19}+q)(a-(-15))& =(\color{red}{q}+\color{orange}{\frac{-5}{19}}).(\color{green}{a}+\color{blue}{15})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(15)} + \color{orange}{(\frac{-5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = aq+15q-\frac{5}{19}a-\frac{5}{19}.15& \text{Uitwerken } \\ & =aq+15q-\frac{5}{19}a-\frac{75}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{14}+q)(\frac{10}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{-17}{14}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2q-\frac{17}{14}a-\frac{17}{14}.2& \text{Uitwerken } \\ & =aq+2q-\frac{17}{14}a-\frac{34}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+2q-\frac{17}{14}a-\frac{17}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-14}{14})(\frac{-8}{11}+a)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{11}q+1a-1.\frac{8}{11}& \text{Uitwerken } \\ & =aq-\frac{8}{11}q+1a-\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-5}{4})(q+(-8))& =(\color{red}{x}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-8)} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = qx-8x+\frac{5}{4}q-\frac{5}{4}.8& \text{Uitwerken } \\ & =qx-8x+\frac{5}{4}q-\frac{40}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-8x+\frac{5}{4}q-10 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-19}{4})(\frac{4}{5}-b)& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{-b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{19}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{5}q-\frac{19}{4}b+\frac{19}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =-bq+\frac{4}{5}q-\frac{19}{4}b+\frac{76}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{4}{5}q-\frac{19}{4}b+\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-24 11:22:48
Een site van Busleyden Atheneum Mechelen