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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-1}{15}+p)(a+\frac{13}{6})& =(\color{red}{p}+\color{orange}{\frac{-1}{15}}).(\color{green}{a}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{6}p-\frac{1}{15}a-\frac{1}{15}.\frac{13}{6}& \text{Uitwerken } \\ & =ap+\frac{13}{6}p-\frac{1}{15}a-\frac{13}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{13}{18})(b+\frac{7}{14})& =(\color{red}{a}+\color{orange}{\frac{13}{18}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a+\frac{13}{18}b+\frac{13}{18}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a+\frac{13}{18}b+\frac{13}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{11}+a)(p-\frac{8}{16})& =(\color{red}{a}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}a-\frac{15}{11}p+\frac{15}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}a-\frac{15}{11}p+\frac{15}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{14}{19})(\frac{3}{20}-x)& =(\color{red}{q}+\color{orange}{\frac{-14}{19}}).(\color{green}{-x}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{20}q+\frac{14}{19}x-\frac{14}{19}.\frac{3}{20}& \text{Uitwerken } \\ & =-qx+\frac{3}{20}q+\frac{14}{19}x-\frac{42}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{3}{20}q+\frac{14}{19}x-\frac{21}{190} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{4}+q)(b-\frac{-16}{7})& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{7}q-4b-4.\frac{16}{7}& \text{Uitwerken } \\ & =bq+\frac{16}{7}q-4b-\frac{64}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-9}{15})(b-\frac{-8}{18})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{9}b+\frac{3}{5}b+\frac{3}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =b^2+(\frac{4}{9}+\frac{3}{5})b+\frac{12}{45} & \text{Neem samen} \\ &=b^2+\frac{47}{45}b+\frac{12}{45} & \text{Maak de som} \\ &=b^2+\frac{47}{45}b+\frac{4}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{9}-q)(\frac{10}{8}+a)& =(\color{red}{-q}+\color{orange}{\frac{-1}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{4}q-\frac{1}{9}a-\frac{1}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq-\frac{5}{4}q-\frac{1}{9}a-\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{6}-p)(p+\frac{-2}{4})& =(\color{red}{-p}+\color{orange}{\frac{7}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{2}p+\frac{7}{3}p-\frac{7}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{2}+\frac{7}{3})p-\frac{7}{6} & \text{Neem samen} \\ &=-p^2+\frac{17}{6}p-\frac{7}{6} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{9}+x)(\frac{20}{2}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -qx+10x+\frac{1}{3}q-\frac{1}{3}.10& \text{Uitwerken } \\ & =-qx+10x+\frac{1}{3}q-\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-1}{16})(\frac{-5}{9}+b)& =(\color{red}{b}+\color{orange}{\frac{1}{16}}).(\color{green}{b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{1}{16})} . \color{green}{(b)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{9}b+\frac{1}{16}b-\frac{1}{16}.\frac{5}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{9})+\frac{1}{16})b-(\frac{-5}{144}) & \text{Neem samen} \\ &=b^2-\frac{71}{144}b-(\frac{-5}{144}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-16}{20})(p+\frac{16}{3})& =(\color{red}{a}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{3}a-\frac{4}{5}p-\frac{4}{5}.\frac{16}{3}& \text{Uitwerken } \\ & =ap+\frac{16}{3}a-\frac{4}{5}p-\frac{64}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{12}-p)(\frac{-4}{6}+p)& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{3}p-\frac{1}{2}p+\frac{1}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{3}+(\frac{-1}{2}))p+(\frac{-2}{6}) & \text{Neem samen} \\ &=-p^2+\frac{1}{6}p+(\frac{-2}{6}) & \text{Maak de som} \\ &=-p^2+\frac{1}{6}p+(\frac{-1}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-10 19:12:34
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