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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{17}+p)(b+\frac{9}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{17}}).(\color{green}{b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{17}p+\frac{1}{17}b+\frac{1}{17}.\frac{9}{17}& \text{Uitwerken } \\ & =bp+\frac{9}{17}p+\frac{1}{17}b+\frac{9}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{8}-b)(x-\frac{-13}{17})& =(\color{red}{-b}+\color{orange}{\frac{-19}{8}}).(\color{green}{x}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{17}b-\frac{19}{8}x-\frac{19}{8}.\frac{13}{17}& \text{Uitwerken } \\ & =-bx-\frac{13}{17}b-\frac{19}{8}x-\frac{247}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{9}-a)(\frac{-18}{20}-x)& =(\color{red}{-a}+\color{orange}{\frac{-20}{9}}).(\color{green}{-x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{10}a+\frac{20}{9}x+\frac{20}{9}.\frac{9}{10}& \text{Uitwerken } \\ & =ax+\frac{9}{10}a+\frac{20}{9}x+\frac{180}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{10}a+\frac{20}{9}x+2 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a+\frac{4}{14})(p+\frac{4}{6})& =(\color{red}{a}+\color{orange}{\frac{2}{7}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{3}a+\frac{2}{7}p+\frac{2}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =ap+\frac{2}{3}a+\frac{2}{7}p+\frac{4}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{20}-b)(a+\frac{-12}{19})& =(\color{red}{-b}+\color{orange}{\frac{-11}{20}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{12}{19}b-\frac{11}{20}a+\frac{11}{20}.\frac{12}{19}& \text{Uitwerken } \\ & =-ab+\frac{12}{19}b-\frac{11}{20}a+\frac{132}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{12}{19}b-\frac{11}{20}a+\frac{33}{95} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{8}{12}-q)(\frac{9}{18}-x)& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q-\frac{2}{3}x+\frac{2}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q-\frac{2}{3}x+\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{1}{2}q-\frac{2}{3}x+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{4}{16})(\frac{4}{15}+q)& =(\color{red}{p}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{15}p+\frac{1}{4}q+\frac{1}{4}.\frac{4}{15}& \text{Uitwerken } \\ & =pq+\frac{4}{15}p+\frac{1}{4}q+\frac{4}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{15}p+\frac{1}{4}q+\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{6}+q)(\frac{6}{3}-p)& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq+2q+\frac{5}{6}p-\frac{5}{6}.2& \text{Uitwerken } \\ & =-pq+2q+\frac{5}{6}p-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+2q+\frac{5}{6}p-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{3}{2})(a+\frac{-12}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}b-\frac{3}{2}a+\frac{3}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}b-\frac{3}{2}a+\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{3}b-\frac{3}{2}a+1 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{19}-p)(\frac{18}{15}-p)& =(\color{red}{-p}+\color{orange}{\frac{1}{19}}).(\color{green}{-p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{1}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{6}{5}p-\frac{1}{19}p+\frac{1}{19}.\frac{6}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-6}{5})+(\frac{-1}{19}))p+\frac{6}{95} & \text{Neem samen} \\ &=p^2-\frac{119}{95}p+\frac{6}{95} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{4}+b)(b+\frac{11}{7})& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{b}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{7}b+\frac{1}{4}b+\frac{1}{4}.\frac{11}{7}& \text{Uitwerken } \\ & =b^2+(\frac{11}{7}+\frac{1}{4})b+\frac{11}{28} & \text{Neem samen} \\ &=b^2+\frac{51}{28}b+\frac{11}{28} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{10}+x)(x+\frac{-9}{14})& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{14}x-\frac{7}{5}x+\frac{7}{5}.\frac{9}{14}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{14})+(\frac{-7}{5}))x+\frac{63}{70} & \text{Neem samen} \\ &=x^2-\frac{143}{70}x+\frac{63}{70} & \text{Maak de som} \\ &=x^2-\frac{143}{70}x+\frac{9}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-20 02:47:12
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