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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-11}{7})(b+\frac{8}{10})& =(\color{red}{p}+\color{orange}{\frac{-11}{7}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}p-\frac{11}{7}b-\frac{11}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}p-\frac{11}{7}b-\frac{44}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{9}-x)(b+\frac{9}{9})& =(\color{red}{-x}+\color{orange}{\frac{2}{9}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1x+\frac{2}{9}b+\frac{2}{9}.1& \text{Uitwerken } \\ & =-bx-1x+\frac{2}{9}b+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{11}{19})(x+\frac{-15}{4})& =(\color{red}{a}+\color{orange}{\frac{-11}{19}}).(\color{green}{x}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{4}a-\frac{11}{19}x+\frac{11}{19}.\frac{15}{4}& \text{Uitwerken } \\ & =ax-\frac{15}{4}a-\frac{11}{19}x+\frac{165}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{5}{10})(p+\frac{13}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{5}a+\frac{1}{2}p+\frac{1}{2}.\frac{13}{5}& \text{Uitwerken } \\ & =ap+\frac{13}{5}a+\frac{1}{2}p+\frac{13}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{4}{7})(\frac{-3}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{2}q-\frac{4}{7}p+\frac{4}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =pq-\frac{1}{2}q-\frac{4}{7}p+\frac{4}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{2}q-\frac{4}{7}p+\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-18}{8})(\frac{-20}{2}-a)& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-10)} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -aa-10a-\frac{9}{4}a-\frac{9}{4}.10& \text{Uitwerken } \\ & =-a^2+((-10)+(\frac{-9}{4}))a-\frac{90}{4} & \text{Neem samen} \\ &=-a^2-\frac{49}{4}a-\frac{90}{4} & \text{Maak de som} \\ &=-a^2-\frac{49}{4}a-\frac{45}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(a+\frac{15}{11})(b-\frac{14}{17})& =(\color{red}{a}+\color{orange}{\frac{15}{11}}).(\color{green}{b}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{15}{11})} . \color{green}{(b)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{14}{17}a+\frac{15}{11}b-\frac{15}{11}.\frac{14}{17}& \text{Uitwerken } \\ & =ab-\frac{14}{17}a+\frac{15}{11}b-\frac{210}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{14}-a)(b+\frac{-10}{8})& =(\color{red}{-a}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{4}a+\frac{2}{7}b-\frac{2}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =-ab+\frac{5}{4}a+\frac{2}{7}b-\frac{10}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{4}a+\frac{2}{7}b-\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{15}+a)(\frac{1}{7}+x)& =(\color{red}{a}+\color{orange}{\frac{-14}{15}}).(\color{green}{x}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{7}a-\frac{14}{15}x-\frac{14}{15}.\frac{1}{7}& \text{Uitwerken } \\ & =ax+\frac{1}{7}a-\frac{14}{15}x-\frac{14}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{7}a-\frac{14}{15}x-\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-1}{3})(a+\frac{-15}{18})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}b-\frac{1}{3}a+\frac{1}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}b-\frac{1}{3}a+\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{12}+b)(q-\frac{13}{13})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b-\frac{1}{3}q+\frac{1}{3}.1& \text{Uitwerken } \\ & =bq-1b-\frac{1}{3}q+\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{11}-b)(a-\frac{14}{6})& =(\color{red}{-b}+\color{orange}{\frac{-3}{11}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{3}b-\frac{3}{11}a+\frac{3}{11}.\frac{7}{3}& \text{Uitwerken } \\ & =-ab+\frac{7}{3}b-\frac{3}{11}a+\frac{21}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{7}{3}b-\frac{3}{11}a+\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-21 13:13:39
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