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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{5}{5})(q+\frac{-6}{15})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{5}p-1q+1.\frac{2}{5}& \text{Uitwerken } \\ & =pq-\frac{2}{5}p-1q+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{20}+b)(b+\frac{1}{10})& =(\color{red}{b}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{10}b-\frac{7}{10}b-\frac{7}{10}.\frac{1}{10}& \text{Uitwerken } \\ & =b^2+(\frac{1}{10}+(\frac{-7}{10}))b-(\frac{-7}{100}) & \text{Neem samen} \\ &=b^2-\frac{6}{10}b-(\frac{-7}{100}) & \text{Maak de som} \\ &=b^2-\frac{3}{5}b+\frac{7}{100} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{3}{8}-a)(q+\frac{-10}{6})& =(\color{red}{-a}+\color{orange}{\frac{3}{8}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{3}a+\frac{3}{8}q-\frac{3}{8}.\frac{5}{3}& \text{Uitwerken } \\ & =-aq+\frac{5}{3}a+\frac{3}{8}q-\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{3}a+\frac{3}{8}q-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-10}{15})(a+\frac{-7}{5})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{5}b-\frac{2}{3}a+\frac{2}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =ab-\frac{7}{5}b-\frac{2}{3}a+\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{14}{8})(a+\frac{6}{9})& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x-\frac{7}{4}a-\frac{7}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x-\frac{7}{4}a-\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x-\frac{7}{4}a-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-11}{5})(\frac{2}{12}-x)& =(\color{red}{a}+\color{orange}{\frac{-11}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{6}a+\frac{11}{5}x-\frac{11}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =-ax+\frac{1}{6}a+\frac{11}{5}x-\frac{11}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{6}{7})(a-\frac{6}{15})& =(\color{red}{a}+\color{orange}{\frac{6}{7}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{5}a+\frac{6}{7}a-\frac{6}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{5})+\frac{6}{7})a-(\frac{-12}{35}) & \text{Neem samen} \\ &=a^2+\frac{16}{35}a-(\frac{-12}{35}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{14}-p)(\frac{5}{2}-b)& =(\color{red}{-p}+\color{orange}{\frac{11}{14}}).(\color{green}{-b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{2}p-\frac{11}{14}b+\frac{11}{14}.\frac{5}{2}& \text{Uitwerken } \\ & =bp-\frac{5}{2}p-\frac{11}{14}b+\frac{55}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{16}{18})(\frac{-13}{18}+a)& =(\color{red}{x}+\color{orange}{\frac{-8}{9}}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{18}x-\frac{8}{9}a+\frac{8}{9}.\frac{13}{18}& \text{Uitwerken } \\ & =ax-\frac{13}{18}x-\frac{8}{9}a+\frac{104}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{13}{18}x-\frac{8}{9}a+\frac{52}{81} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{4}{2}-a)(\frac{-5}{10}-b)& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-2b-2.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-2b-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{2}a-2b-1 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{13}-p)(\frac{-10}{9}-b)& =(\color{red}{-p}+\color{orange}{\frac{-12}{13}}).(\color{green}{-b}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{9}p+\frac{12}{13}b+\frac{12}{13}.\frac{10}{9}& \text{Uitwerken } \\ & =bp+\frac{10}{9}p+\frac{12}{13}b+\frac{120}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{10}{9}p+\frac{12}{13}b+\frac{40}{39} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{12}-a)(q-\frac{-17}{14})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{14}a+1q+1.\frac{17}{14}& \text{Uitwerken } \\ & =-aq-\frac{17}{14}a+1q+\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-29 22:18:08
Een site van Busleyden Atheneum Mechelen