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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-6}{13}+b)(p+\frac{-1}{12})& =(\color{red}{b}+\color{orange}{\frac{-6}{13}}).(\color{green}{p}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{12}b-\frac{6}{13}p+\frac{6}{13}.\frac{1}{12}& \text{Uitwerken } \\ & =bp-\frac{1}{12}b-\frac{6}{13}p+\frac{6}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{12}b-\frac{6}{13}p+\frac{1}{26} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{20}{17})(\frac{-17}{3}-b)& =(\color{red}{a}+\color{orange}{\frac{-20}{17}}).(\color{green}{-b}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{3}a+\frac{20}{17}b+\frac{20}{17}.\frac{17}{3}& \text{Uitwerken } \\ & =-ab-\frac{17}{3}a+\frac{20}{17}b+\frac{340}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{17}{3}a+\frac{20}{17}b+\frac{20}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{5}+p)(\frac{13}{5}-a)& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{-a}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(-3)} . \color{green}{(-a)} + \color{orange}{(-3)} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{5}p+3a-3.\frac{13}{5}& \text{Uitwerken } \\ & =-ap+\frac{13}{5}p+3a-\frac{39}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-(-11))(\frac{17}{10}+x)& =(\color{red}{p}+\color{orange}{11}).(\color{green}{x}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(11)} . \color{green}{(x)} + \color{orange}{(11)} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{10}p+11x+11.\frac{17}{10}& \text{Uitwerken } \\ & =px+\frac{17}{10}p+11x+\frac{187}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{16}-x)(\frac{-2}{19}-a)& =(\color{red}{-x}+\color{orange}{\frac{-1}{8}}).(\color{green}{-a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{19}x+\frac{1}{8}a+\frac{1}{8}.\frac{2}{19}& \text{Uitwerken } \\ & =ax+\frac{2}{19}x+\frac{1}{8}a+\frac{2}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{19}x+\frac{1}{8}a+\frac{1}{76} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{10}{8})(x+\frac{9}{20})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{20}x-\frac{5}{4}x-\frac{5}{4}.\frac{9}{20}& \text{Uitwerken } \\ & =x^2+(\frac{9}{20}+(\frac{-5}{4}))x-(\frac{-45}{80}) & \text{Neem samen} \\ &=x^2-\frac{16}{20}x-(\frac{-45}{80}) & \text{Maak de som} \\ &=x^2-\frac{4}{5}x+\frac{9}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{2}-a)(\frac{2}{9}-p)& =(\color{red}{-a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-p}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{9}a+\frac{3}{2}p-\frac{3}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =ap-\frac{2}{9}a+\frac{3}{2}p-\frac{6}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{9}a+\frac{3}{2}p-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{6}+a)(\frac{-7}{14}+b)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a+3b-3.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a+3b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-14}{13})(q-\frac{-1}{3})& =(\color{red}{a}+\color{orange}{\frac{-14}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{3}a-\frac{14}{13}q-\frac{14}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =aq+\frac{1}{3}a-\frac{14}{13}q-\frac{14}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{12}+x)(4-b)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bx+4x-\frac{3}{4}b+\frac{3}{4}.4& \text{Uitwerken } \\ & =-bx+4x-\frac{3}{4}b+\frac{12}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+4x-\frac{3}{4}b+3 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}((-6)-x)(\frac{-12}{14}-q)& =(\color{red}{-x}+\color{orange}{(-6)}).(\color{green}{-q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(-6)} . \color{green}{(-q)} + \color{orange}{(-6)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{7}x+6q+6.\frac{6}{7}& \text{Uitwerken } \\ & =qx+\frac{6}{7}x+6q+\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{4}+b)(q-\frac{17}{11})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{11}b+\frac{1}{2}q-\frac{1}{2}.\frac{17}{11}& \text{Uitwerken } \\ & =bq-\frac{17}{11}b+\frac{1}{2}q-\frac{17}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-11 16:03:01
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