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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-5}{8})(\frac{15}{4}-a)& =(\color{red}{b}+\color{orange}{\frac{5}{8}}).(\color{green}{-a}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{5}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{15}{4}b-\frac{5}{8}a+\frac{5}{8}.\frac{15}{4}& \text{Uitwerken } \\ & =-ab+\frac{15}{4}b-\frac{5}{8}a+\frac{75}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{16}{3}-a)(\frac{8}{4}-q)& =(\color{red}{-a}+\color{orange}{\frac{16}{3}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{16}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq-2a-\frac{16}{3}q+\frac{16}{3}.2& \text{Uitwerken } \\ & =aq-2a-\frac{16}{3}q+\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-13}{19}-p)(\frac{-7}{8}+b)& =(\color{red}{-p}+\color{orange}{\frac{-13}{19}}).(\color{green}{b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{8}p-\frac{13}{19}b+\frac{13}{19}.\frac{7}{8}& \text{Uitwerken } \\ & =-bp+\frac{7}{8}p-\frac{13}{19}b+\frac{91}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-6}{12})(\frac{6}{12}+a)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p-\frac{1}{2}a-\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p-\frac{1}{2}a-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{7}-p)(x+\frac{4}{11})& =(\color{red}{-p}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{11}p-\frac{2}{7}x-\frac{2}{7}.\frac{4}{11}& \text{Uitwerken } \\ & =-px-\frac{4}{11}p-\frac{2}{7}x-\frac{8}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{16}{4})(\frac{-12}{16}+x)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{4}a+4x-4.\frac{3}{4}& \text{Uitwerken } \\ & =ax-\frac{3}{4}a+4x-\frac{12}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{4}a+4x-3 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-19}{20}-a)(\frac{5}{9}+b)& =(\color{red}{-a}+\color{orange}{\frac{-19}{20}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{9}a-\frac{19}{20}b-\frac{19}{20}.\frac{5}{9}& \text{Uitwerken } \\ & =-ab-\frac{5}{9}a-\frac{19}{20}b-\frac{95}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{5}{9}a-\frac{19}{20}b-\frac{19}{36} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{18}{4})(q-\frac{5}{15})& =(\color{red}{b}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}b+\frac{9}{2}q-\frac{9}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}b+\frac{9}{2}q-\frac{9}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{3}b+\frac{9}{2}q-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-8}{6}+q)(q+\frac{-14}{4})& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{2}q-\frac{4}{3}q+\frac{4}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{2})+(\frac{-4}{3}))q+\frac{28}{6} & \text{Neem samen} \\ &=q^2-\frac{29}{6}q+\frac{28}{6} & \text{Maak de som} \\ &=q^2-\frac{29}{6}q+\frac{14}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(p+\frac{15}{13})(q-\frac{-12}{14})& =(\color{red}{p}+\color{orange}{\frac{15}{13}}).(\color{green}{q}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{7}p+\frac{15}{13}q+\frac{15}{13}.\frac{6}{7}& \text{Uitwerken } \\ & =pq+\frac{6}{7}p+\frac{15}{13}q+\frac{90}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{12}{15})(a+\frac{14}{10})& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{5}x-\frac{4}{5}a-\frac{4}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =ax+\frac{7}{5}x-\frac{4}{5}a-\frac{28}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-9}{8}+b)(q-\frac{-15}{4})& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{4}b-\frac{9}{8}q-\frac{9}{8}.\frac{15}{4}& \text{Uitwerken } \\ & =bq+\frac{15}{4}b-\frac{9}{8}q-\frac{135}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-12 19:36:26
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