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

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  1. \((\frac{20}{14}-a)(\frac{7}{18}+p)\)
  2. \((\frac{16}{14}-x)(\frac{13}{15}-p)\)
  3. \((\frac{-14}{19}+a)(x+\frac{17}{18})\)
  4. \((q-\frac{-9}{19})(\frac{16}{9}+q)\)
  5. \((\frac{-15}{4}+q)(\frac{-11}{7}-a)\)
  6. \((\frac{2}{7}+x)(\frac{4}{9}+q)\)
  7. \((b+\frac{-17}{14})(p+\frac{6}{19})\)
  8. \((\frac{1}{6}-q)(x-10)\)
  9. \((q+\frac{18}{6})(b-\frac{4}{17})\)
  10. \((\frac{12}{2}+a)(q+\frac{20}{10})\)
  11. \((\frac{-2}{15}+b)(a-\frac{5}{5})\)
  12. \((a-\frac{-18}{19})(q+\frac{-8}{19})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{14}-a)(\frac{7}{18}+p)& =(\color{red}{-a}+\color{orange}{\frac{10}{7}}).(\color{green}{p}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{18}a+\frac{10}{7}p+\frac{10}{7}.\frac{7}{18}& \text{Uitwerken } \\ & =-ap-\frac{7}{18}a+\frac{10}{7}p+\frac{70}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{18}a+\frac{10}{7}p+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{16}{14}-x)(\frac{13}{15}-p)& =(\color{red}{-x}+\color{orange}{\frac{8}{7}}).(\color{green}{-p}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{8}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{15}x-\frac{8}{7}p+\frac{8}{7}.\frac{13}{15}& \text{Uitwerken } \\ & =px-\frac{13}{15}x-\frac{8}{7}p+\frac{104}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-14}{19}+a)(x+\frac{17}{18})& =(\color{red}{a}+\color{orange}{\frac{-14}{19}}).(\color{green}{x}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{18}a-\frac{14}{19}x-\frac{14}{19}.\frac{17}{18}& \text{Uitwerken } \\ & =ax+\frac{17}{18}a-\frac{14}{19}x-\frac{238}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{18}a-\frac{14}{19}x-\frac{119}{171} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-9}{19})(\frac{16}{9}+q)& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{q}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{16}{9}q+\frac{9}{19}q+\frac{9}{19}.\frac{16}{9}& \text{Uitwerken } \\ & =q^2+(\frac{16}{9}+\frac{9}{19})q+\frac{144}{171} & \text{Neem samen} \\ &=q^2+\frac{385}{171}q+\frac{144}{171} & \text{Maak de som} \\ &=q^2+\frac{385}{171}q+\frac{16}{19} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{4}+q)(\frac{-11}{7}-a)& =(\color{red}{q}+\color{orange}{\frac{-15}{4}}).(\color{green}{-a}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{7}q+\frac{15}{4}a+\frac{15}{4}.\frac{11}{7}& \text{Uitwerken } \\ & =-aq-\frac{11}{7}q+\frac{15}{4}a+\frac{165}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{7}+x)(\frac{4}{9}+q)& =(\color{red}{x}+\color{orange}{\frac{2}{7}}).(\color{green}{q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{2}{7})} . \color{green}{(q)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{9}x+\frac{2}{7}q+\frac{2}{7}.\frac{4}{9}& \text{Uitwerken } \\ & =qx+\frac{4}{9}x+\frac{2}{7}q+\frac{8}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-17}{14})(p+\frac{6}{19})& =(\color{red}{b}+\color{orange}{\frac{-17}{14}}).(\color{green}{p}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{6}{19}b-\frac{17}{14}p-\frac{17}{14}.\frac{6}{19}& \text{Uitwerken } \\ & =bp+\frac{6}{19}b-\frac{17}{14}p-\frac{102}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{6}{19}b-\frac{17}{14}p-\frac{51}{133} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{6}-q)(x-10)& =(\color{red}{-q}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-10)} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -qx+10q+\frac{1}{6}x-\frac{1}{6}.10& \text{Uitwerken } \\ & =-qx+10q+\frac{1}{6}x-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+10q+\frac{1}{6}x-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{18}{6})(b-\frac{4}{17})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{17}q+3b-3.\frac{4}{17}& \text{Uitwerken } \\ & =bq-\frac{4}{17}q+3b-\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{2}+a)(q+\frac{20}{10})& =(\color{red}{a}+\color{orange}{6}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+6q+6.2& \text{Uitwerken } \\ & =aq+2a+6q+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{15}+b)(a-\frac{5}{5})& =(\color{red}{b}+\color{orange}{\frac{-2}{15}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b-\frac{2}{15}a+\frac{2}{15}.1& \text{Uitwerken } \\ & =ab-1b-\frac{2}{15}a+\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-18}{19})(q+\frac{-8}{19})& =(\color{red}{a}+\color{orange}{\frac{18}{19}}).(\color{green}{q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{19}a+\frac{18}{19}q-\frac{18}{19}.\frac{8}{19}& \text{Uitwerken } \\ & =aq-\frac{8}{19}a+\frac{18}{19}q-\frac{144}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-15 02:02:51
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