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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{-13}{2})(q-\frac{-8}{9})& =(\color{red}{q}+\color{orange}{\frac{-13}{2}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{9}q-\frac{13}{2}q-\frac{13}{2}.\frac{8}{9}& \text{Uitwerken } \\ & =q^2+(\frac{8}{9}+(\frac{-13}{2}))q-(\frac{-104}{18}) & \text{Neem samen} \\ &=q^2-\frac{101}{18}q-(\frac{-104}{18}) & \text{Maak de som} \\ &=q^2-\frac{101}{18}q+\frac{52}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(p-\frac{15}{12})(\frac{19}{6}+a)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{6}p-\frac{5}{4}a-\frac{5}{4}.\frac{19}{6}& \text{Uitwerken } \\ & =ap+\frac{19}{6}p-\frac{5}{4}a-\frac{95}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-18}{16})(x+\frac{-6}{18})& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}a-\frac{9}{8}x+\frac{9}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}a-\frac{9}{8}x+\frac{9}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{3}a-\frac{9}{8}x+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{14}+b)(\frac{-7}{16}-a)& =(\color{red}{b}+\color{orange}{\frac{-9}{14}}).(\color{green}{-a}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{16}b+\frac{9}{14}a+\frac{9}{14}.\frac{7}{16}& \text{Uitwerken } \\ & =-ab-\frac{7}{16}b+\frac{9}{14}a+\frac{63}{224} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{7}{16}b+\frac{9}{14}a+\frac{9}{32} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-1}{15})(\frac{-4}{15}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{-q}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{15}b+\frac{1}{15}q+\frac{1}{15}.\frac{4}{15}& \text{Uitwerken } \\ & =-bq-\frac{4}{15}b+\frac{1}{15}q+\frac{4}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-10}{7})(b-\frac{16}{3})& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{3}x+\frac{10}{7}b-\frac{10}{7}.\frac{16}{3}& \text{Uitwerken } \\ & =bx-\frac{16}{3}x+\frac{10}{7}b-\frac{160}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{4}+b)(b-\frac{-13}{11})& =(\color{red}{b}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{11}b+\frac{9}{4}b+\frac{9}{4}.\frac{13}{11}& \text{Uitwerken } \\ & =b^2+(\frac{13}{11}+\frac{9}{4})b+\frac{117}{44} & \text{Neem samen} \\ &=b^2+\frac{151}{44}b+\frac{117}{44} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{20}-a)(\frac{11}{5}-x)& =(\color{red}{-a}+\color{orange}{\frac{-3}{20}}).(\color{green}{-x}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{5}a+\frac{3}{20}x-\frac{3}{20}.\frac{11}{5}& \text{Uitwerken } \\ & =ax-\frac{11}{5}a+\frac{3}{20}x-\frac{33}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{10}+x)(q-\frac{14}{13})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{13}x+\frac{2}{5}q-\frac{2}{5}.\frac{14}{13}& \text{Uitwerken } \\ & =qx-\frac{14}{13}x+\frac{2}{5}q-\frac{28}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-9}{16})(x-\frac{2}{8})& =(\color{red}{a}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}a+\frac{9}{16}x-\frac{9}{16}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}a+\frac{9}{16}x-\frac{9}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{8}-x)(q-\frac{19}{11})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{11}x-\frac{1}{2}q+\frac{1}{2}.\frac{19}{11}& \text{Uitwerken } \\ & =-qx+\frac{19}{11}x-\frac{1}{2}q+\frac{19}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{4}+b)(\frac{12}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{5}b-\frac{9}{4}a-\frac{9}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =ab+\frac{4}{5}b-\frac{9}{4}a-\frac{36}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{5}b-\frac{9}{4}a-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-29 02:03:59
Een site van Busleyden Atheneum Mechelen