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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-6}{5})(\frac{16}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-a}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{8}{7}a-\frac{6}{5}a+\frac{6}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{8}{7}+(\frac{-6}{5}))a+(\frac{-48}{35}) & \text{Neem samen} \\ &=-a^2-\frac{2}{35}a+(\frac{-48}{35}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{3}-p)(\frac{12}{12}+p)& =(\color{red}{-p}+\color{orange}{\frac{-14}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{-14}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p-\frac{14}{3}p-\frac{14}{3}.1& \text{Uitwerken } \\ & =-p^2+((-1)+(\frac{-14}{3}))p-\frac{14}{3} & \text{Neem samen} \\ &=-p^2-\frac{17}{3}p-\frac{14}{3} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{2}{9})(q-\frac{18}{13})& =(\color{red}{b}+\color{orange}{\frac{2}{9}}).(\color{green}{q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{2}{9})} . \color{green}{(q)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{13}b+\frac{2}{9}q-\frac{2}{9}.\frac{18}{13}& \text{Uitwerken } \\ & =bq-\frac{18}{13}b+\frac{2}{9}q-\frac{36}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{18}{13}b+\frac{2}{9}q-\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-5}{8})(q+\frac{-6}{8})& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{4}p+\frac{5}{8}q-\frac{5}{8}.\frac{3}{4}& \text{Uitwerken } \\ & =pq-\frac{3}{4}p+\frac{5}{8}q-\frac{15}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-6}{14})(\frac{-6}{2}+x)& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3a+\frac{3}{7}x-\frac{3}{7}.3& \text{Uitwerken } \\ & =ax-3a+\frac{3}{7}x-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{1}{7})(p+\frac{-4}{11})& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{p}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{11}x-\frac{1}{7}p+\frac{1}{7}.\frac{4}{11}& \text{Uitwerken } \\ & =px-\frac{4}{11}x-\frac{1}{7}p+\frac{4}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{11}+b)(a-\frac{2}{14})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{7}b+1a-1.\frac{1}{7}& \text{Uitwerken } \\ & =ab-\frac{1}{7}b+1a-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{2}-q)(q+\frac{20}{14})& =(\color{red}{-q}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{10}{7}q-5q-5.\frac{10}{7}& \text{Uitwerken } \\ & =-q^2+((\frac{-10}{7})+(-5))q-\frac{50}{7} & \text{Neem samen} \\ &=-q^2-\frac{45}{7}q-\frac{50}{7} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{2}+x)(\frac{17}{8}+a)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{8}x+2a+2.\frac{17}{8}& \text{Uitwerken } \\ & =ax+\frac{17}{8}x+2a+\frac{34}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{8}x+2a+\frac{17}{4} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{13}{3})(p+\frac{20}{5})& =(\color{red}{q}+\color{orange}{\frac{-13}{3}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{-13}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4q-\frac{13}{3}p-\frac{13}{3}.4& \text{Uitwerken } \\ & =pq+4q-\frac{13}{3}p-\frac{52}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{19}{17})(b-\frac{5}{6})& =(\color{red}{b}+\color{orange}{\frac{19}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{19}{17})} . \color{green}{(b)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{6}b+\frac{19}{17}b-\frac{19}{17}.\frac{5}{6}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{6})+\frac{19}{17})b-(\frac{-95}{102}) & \text{Neem samen} \\ &=b^2+\frac{29}{102}b-(\frac{-95}{102}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{11}+b)(p+\frac{-11}{17})& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{p}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{17}b-\frac{2}{11}p+\frac{2}{11}.\frac{11}{17}& \text{Uitwerken } \\ & =bp-\frac{11}{17}b-\frac{2}{11}p+\frac{22}{187} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{11}{17}b-\frac{2}{11}p+\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)
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