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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{15}-b)(\frac{-4}{12}-b)& =(\color{red}{-b}+\color{orange}{\frac{-4}{15}}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b+\frac{4}{15}b+\frac{4}{15}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+\frac{4}{15})b+\frac{4}{45} & \text{Neem samen} \\ &=b^2+\frac{9}{15}b+\frac{4}{45} & \text{Maak de som} \\ &=b^2+\frac{3}{5}b+\frac{4}{45} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a-\frac{12}{3})(q-\frac{-20}{16})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{4}a-4q-4.\frac{5}{4}& \text{Uitwerken } \\ & =aq+\frac{5}{4}a-4q-\frac{20}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{4}a-4q-5 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-13}{20})(\frac{-1}{3}+a)& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}x-\frac{13}{20}a+\frac{13}{20}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}x-\frac{13}{20}a+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{15}+q)(\frac{-15}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{-p}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{13}q-\frac{4}{5}p-\frac{4}{5}.\frac{15}{13}& \text{Uitwerken } \\ & =-pq-\frac{15}{13}q-\frac{4}{5}p-\frac{60}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{15}{13}q-\frac{4}{5}p-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{14}{17})(\frac{-5}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-14}{17}}).(\color{green}{-p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{3}b+\frac{14}{17}p+\frac{14}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-bp-\frac{1}{3}b+\frac{14}{17}p+\frac{14}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{1}{12})(q+\frac{-20}{13})& =(\color{red}{x}+\color{orange}{\frac{-1}{12}}).(\color{green}{q}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{20}{13}x-\frac{1}{12}q+\frac{1}{12}.\frac{20}{13}& \text{Uitwerken } \\ & =qx-\frac{20}{13}x-\frac{1}{12}q+\frac{20}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{20}{13}x-\frac{1}{12}q+\frac{5}{39} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{3}-x)(q-\frac{14}{10})& =(\color{red}{-x}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{5}x+\frac{7}{3}q-\frac{7}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =-qx+\frac{7}{5}x+\frac{7}{3}q-\frac{49}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{11}{3})(p+\frac{15}{3})& =(\color{red}{b}+\color{orange}{\frac{11}{3}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{11}{3})} . \color{green}{(p)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bp+5b+\frac{11}{3}p+\frac{11}{3}.5& \text{Uitwerken } \\ & =bp+5b+\frac{11}{3}p+\frac{55}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{11}+a)(p-\frac{11}{20})& =(\color{red}{a}+\color{orange}{\frac{-3}{11}}).(\color{green}{p}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{20}a-\frac{3}{11}p+\frac{3}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =ap-\frac{11}{20}a-\frac{3}{11}p+\frac{33}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{20}a-\frac{3}{11}p+\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{18}+q)(\frac{-16}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{9}q-\frac{8}{9}x+\frac{8}{9}.\frac{8}{9}& \text{Uitwerken } \\ & =qx-\frac{8}{9}q-\frac{8}{9}x+\frac{64}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{14}{20})(q+\frac{5}{7})& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{7}p+\frac{7}{10}q+\frac{7}{10}.\frac{5}{7}& \text{Uitwerken } \\ & =pq+\frac{5}{7}p+\frac{7}{10}q+\frac{35}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{7}p+\frac{7}{10}q+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{8}+x)(x+\frac{7}{11})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{11}x+\frac{3}{4}x+\frac{3}{4}.\frac{7}{11}& \text{Uitwerken } \\ & =x^2+(\frac{7}{11}+\frac{3}{4})x+\frac{21}{44} & \text{Neem samen} \\ &=x^2+\frac{61}{44}x+\frac{21}{44} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-18 06:34:04
Een site van Busleyden Atheneum Mechelen