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

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Werk uit en vereenvoudig

  1. \((\frac{12}{18}+p)(\frac{-18}{5}+q)\)
  2. \((b+\frac{9}{19})(a-\frac{6}{10})\)
  3. \((\frac{-7}{9}-x)(\frac{-5}{20}+q)\)
  4. \((\frac{15}{11}-a)((-19)-a)\)
  5. \((\frac{-6}{2}+q)(\frac{-3}{14}+p)\)
  6. \((\frac{-17}{3}+b)(\frac{8}{10}-p)\)
  7. \((\frac{20}{6}-q)(\frac{-19}{5}-b)\)
  8. \((a+\frac{11}{9})(p+\frac{12}{10})\)
  9. \((\frac{4}{12}-x)(x+\frac{18}{5})\)
  10. \((x-\frac{-10}{3})(b+\frac{9}{5})\)
  11. \((\frac{-3}{16}+x)(x-\frac{-5}{4})\)
  12. \((\frac{11}{7}-x)(\frac{17}{20}-p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{18}+p)(\frac{-18}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{18}{5}p+\frac{2}{3}q-\frac{2}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =pq-\frac{18}{5}p+\frac{2}{3}q-\frac{36}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{18}{5}p+\frac{2}{3}q-\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{9}{19})(a-\frac{6}{10})& =(\color{red}{b}+\color{orange}{\frac{9}{19}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{5}b+\frac{9}{19}a-\frac{9}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =ab-\frac{3}{5}b+\frac{9}{19}a-\frac{27}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{9}-x)(\frac{-5}{20}+q)& =(\color{red}{-x}+\color{orange}{\frac{-7}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{4}x-\frac{7}{9}q+\frac{7}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-qx+\frac{1}{4}x-\frac{7}{9}q+\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{11}-a)((-19)-a)& =(\color{red}{-a}+\color{orange}{\frac{15}{11}}).(\color{green}{-a}+\color{blue}{(-19)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(-19)} + \color{orange}{(\frac{15}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = aa+19a-\frac{15}{11}a-\frac{15}{11}.19& \text{Uitwerken } \\ & =a^2+(19+(\frac{-15}{11}))a-(\frac{-285}{11}) & \text{Neem samen} \\ &=a^2+\frac{194}{11}a-(\frac{-285}{11}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{2}+q)(\frac{-3}{14}+p)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{14}q-3p+3.\frac{3}{14}& \text{Uitwerken } \\ & =pq-\frac{3}{14}q-3p+\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-17}{3}+b)(\frac{8}{10}-p)& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{-p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{4}{5}b+\frac{17}{3}p-\frac{17}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =-bp+\frac{4}{5}b+\frac{17}{3}p-\frac{68}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{6}-q)(\frac{-19}{5}-b)& =(\color{red}{-q}+\color{orange}{\frac{10}{3}}).(\color{green}{-b}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{5}q-\frac{10}{3}b-\frac{10}{3}.\frac{19}{5}& \text{Uitwerken } \\ & =bq+\frac{19}{5}q-\frac{10}{3}b-\frac{190}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{19}{5}q-\frac{10}{3}b-\frac{38}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{11}{9})(p+\frac{12}{10})& =(\color{red}{a}+\color{orange}{\frac{11}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{5}a+\frac{11}{9}p+\frac{11}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =ap+\frac{6}{5}a+\frac{11}{9}p+\frac{66}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{5}a+\frac{11}{9}p+\frac{22}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{12}-x)(x+\frac{18}{5})& =(\color{red}{-x}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{18}{5}x+\frac{1}{3}x+\frac{1}{3}.\frac{18}{5}& \text{Uitwerken } \\ & =-x^2+((\frac{-18}{5})+\frac{1}{3})x+(\frac{-18}{15}) & \text{Neem samen} \\ &=-x^2-\frac{49}{15}x+(\frac{-18}{15}) & \text{Maak de som} \\ &=-x^2-\frac{49}{15}x+(\frac{-6}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-10}{3})(b+\frac{9}{5})& =(\color{red}{x}+\color{orange}{\frac{10}{3}}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{5}x+\frac{10}{3}b+\frac{10}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =bx+\frac{9}{5}x+\frac{10}{3}b+\frac{90}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{5}x+\frac{10}{3}b+6 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{16}+x)(x-\frac{-5}{4})& =(\color{red}{x}+\color{orange}{\frac{-3}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{4}x-\frac{3}{16}x-\frac{3}{16}.\frac{5}{4}& \text{Uitwerken } \\ & =x^2+(\frac{5}{4}+(\frac{-3}{16}))x-(\frac{-15}{64}) & \text{Neem samen} \\ &=x^2+\frac{17}{16}x-(\frac{-15}{64}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{11}{7}-x)(\frac{17}{20}-p)& =(\color{red}{-x}+\color{orange}{\frac{11}{7}}).(\color{green}{-p}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{11}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{20}x-\frac{11}{7}p+\frac{11}{7}.\frac{17}{20}& \text{Uitwerken } \\ & =px-\frac{17}{20}x-\frac{11}{7}p+\frac{187}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-05 09:49:45
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