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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{14}+b)(b+\frac{-18}{18})& =(\color{red}{b}+\color{orange}{\frac{1}{14}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{14})} . \color{green}{(b)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bb-1b+\frac{1}{14}b-\frac{1}{14}.1& \text{Uitwerken } \\ & =b^2+((-1)+\frac{1}{14})b-(\frac{-1}{14}) & \text{Neem samen} \\ &=b^2-\frac{13}{14}b-(\frac{-1}{14}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-16}{4})(b+\frac{-2}{17})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{17}a-4b+4.\frac{2}{17}& \text{Uitwerken } \\ & =ab-\frac{2}{17}a-4b+\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{6}+a)(\frac{17}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1a+\frac{1}{6}q+\frac{1}{6}.1& \text{Uitwerken } \\ & =aq+1a+\frac{1}{6}q+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{14}{6})(\frac{-2}{3}+x)& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{2}{3}x+\frac{7}{3}x-\frac{7}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =x^2+((\frac{-2}{3})+\frac{7}{3})x-(\frac{-14}{9}) & \text{Neem samen} \\ &=x^2+\frac{5}{3}x-(\frac{-14}{9}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{9}+p)(a-\frac{18}{13})& =(\color{red}{p}+\color{orange}{\frac{14}{9}}).(\color{green}{a}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{13}p+\frac{14}{9}a-\frac{14}{9}.\frac{18}{13}& \text{Uitwerken } \\ & =ap-\frac{18}{13}p+\frac{14}{9}a-\frac{252}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{18}{13}p+\frac{14}{9}a-\frac{28}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{16}-a)(p-\frac{13}{14})& =(\color{red}{-a}+\color{orange}{\frac{7}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{14}a+\frac{7}{16}p-\frac{7}{16}.\frac{13}{14}& \text{Uitwerken } \\ & =-ap+\frac{13}{14}a+\frac{7}{16}p-\frac{91}{224} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{13}{14}a+\frac{7}{16}p-\frac{13}{32} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-4}{18})(q-\frac{7}{17})& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{q}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{17}q+\frac{2}{9}q-\frac{2}{9}.\frac{7}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{17})+\frac{2}{9})q-(\frac{-14}{153}) & \text{Neem samen} \\ &=q^2-\frac{29}{153}q-(\frac{-14}{153}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{13}{20}+x)(\frac{-12}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{13}{20}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{13}{20})} . \color{green}{(q)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4x+\frac{13}{20}q-\frac{13}{20}.4& \text{Uitwerken } \\ & =qx-4x+\frac{13}{20}q-\frac{52}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-4x+\frac{13}{20}q-\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{16}+x)(\frac{-1}{4}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}x-\frac{5}{16}a+\frac{5}{16}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}x-\frac{5}{16}a+\frac{5}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{9}-x)(\frac{-17}{15}-a)& =(\color{red}{-x}+\color{orange}{\frac{10}{9}}).(\color{green}{-a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{15}x-\frac{10}{9}a-\frac{10}{9}.\frac{17}{15}& \text{Uitwerken } \\ & =ax+\frac{17}{15}x-\frac{10}{9}a-\frac{170}{135} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{15}x-\frac{10}{9}a-\frac{34}{27} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b-\frac{4}{16})(\frac{-3}{20}-x)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-x}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{20}b+\frac{1}{4}x+\frac{1}{4}.\frac{3}{20}& \text{Uitwerken } \\ & =-bx-\frac{3}{20}b+\frac{1}{4}x+\frac{3}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{14}{5})(x-8)& =(\color{red}{p}+\color{orange}{\frac{14}{5}}).(\color{green}{x}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-8)} + \color{orange}{(\frac{14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = px-8p+\frac{14}{5}x-\frac{14}{5}.8& \text{Uitwerken } \\ & =px-8p+\frac{14}{5}x-\frac{112}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-14 12:43:56
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