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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-9}{4}-q)(\frac{7}{4}-q)& =(\color{red}{-q}+\color{orange}{\frac{-9}{4}}).(\color{green}{-q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{4}q+\frac{9}{4}q-\frac{9}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{4})+\frac{9}{4})q-(\frac{-63}{16}) & \text{Neem samen} \\ &=q^2+\frac{2}{4}q-(\frac{-63}{16}) & \text{Maak de som} \\ &=q^2+\frac{1}{2}q+\frac{63}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(p+\frac{6}{20})(\frac{-11}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{6}p+\frac{3}{10}b-\frac{3}{10}.\frac{11}{6}& \text{Uitwerken } \\ & =bp-\frac{11}{6}p+\frac{3}{10}b-\frac{33}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{11}{6}p+\frac{3}{10}b-\frac{11}{20} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-5}{18})(b+\frac{14}{7})& =(\color{red}{b}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b-\frac{5}{18}b-\frac{5}{18}.2& \text{Uitwerken } \\ & =b^2+(2+(\frac{-5}{18}))b-(\frac{-10}{18}) & \text{Neem samen} \\ &=b^2+\frac{31}{18}b-(\frac{-10}{18}) & \text{Maak de som} \\ &=b^2+\frac{31}{18}b+\frac{5}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{5}+x)(\frac{-12}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -qx-3x+\frac{2}{5}q+\frac{2}{5}.3& \text{Uitwerken } \\ & =-qx-3x+\frac{2}{5}q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{9}+q)(\frac{-20}{16}+x)& =(\color{red}{q}+\color{orange}{\frac{-16}{9}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{4}q-\frac{16}{9}x+\frac{16}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =qx-\frac{5}{4}q-\frac{16}{9}x+\frac{80}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{4}q-\frac{16}{9}x+\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-7}{7})(b+\frac{-7}{20})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{20}p-1b+1.\frac{7}{20}& \text{Uitwerken } \\ & =bp-\frac{7}{20}p-1b+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{6}-q)(q+\frac{11}{4})& =(\color{red}{-q}+\color{orange}{\frac{-8}{3}}).(\color{green}{q}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{11}{4}q-\frac{8}{3}q-\frac{8}{3}.\frac{11}{4}& \text{Uitwerken } \\ & =-q^2+((\frac{-11}{4})+(\frac{-8}{3}))q-\frac{88}{12} & \text{Neem samen} \\ &=-q^2-\frac{65}{12}q-\frac{88}{12} & \text{Maak de som} \\ &=-q^2-\frac{65}{12}q-\frac{22}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{8}+a)(a-\frac{5}{20})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{4}a+\frac{3}{2}a-\frac{3}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{4})+\frac{3}{2})a-(\frac{-3}{8}) & \text{Neem samen} \\ &=a^2+\frac{5}{4}a-(\frac{-3}{8}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{5}+b)(\frac{4}{18}-q)& =(\color{red}{b}+\color{orange}{\frac{18}{5}}).(\color{green}{-q}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{18}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{9}b-\frac{18}{5}q+\frac{18}{5}.\frac{2}{9}& \text{Uitwerken } \\ & =-bq+\frac{2}{9}b-\frac{18}{5}q+\frac{36}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{2}{9}b-\frac{18}{5}q+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a+(-14))(b-\frac{7}{2})& =(\color{red}{a}+\color{orange}{(-14)}).(\color{green}{b}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(-14)} . \color{green}{(b)} + \color{orange}{(-14)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{2}a-14b+14.\frac{7}{2}& \text{Uitwerken } \\ & =ab-\frac{7}{2}a-14b+\frac{98}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{7}{2}a-14b+49 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{4}+b)(q+\frac{18}{11})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{11}b-2q-2.\frac{18}{11}& \text{Uitwerken } \\ & =bq+\frac{18}{11}b-2q-\frac{36}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{7}+a)(b-\frac{11}{13})& =(\color{red}{a}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{13}a-\frac{6}{7}b+\frac{6}{7}.\frac{11}{13}& \text{Uitwerken } \\ & =ab-\frac{11}{13}a-\frac{6}{7}b+\frac{66}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-21 05:29:39
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