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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{9}+p)(a+\frac{-4}{16})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{4}p+1a-1.\frac{1}{4}& \text{Uitwerken } \\ & =ap-\frac{1}{4}p+1a-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{5}{13})(q+\frac{-12}{5})& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{q}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{5}{13})} . \color{green}{(q)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{12}{5}b+\frac{5}{13}q-\frac{5}{13}.\frac{12}{5}& \text{Uitwerken } \\ & =bq-\frac{12}{5}b+\frac{5}{13}q-\frac{60}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{12}{5}b+\frac{5}{13}q-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{7}+x)(b-2)& =(\color{red}{x}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2x+\frac{18}{7}b-\frac{18}{7}.2& \text{Uitwerken } \\ & =bx-2x+\frac{18}{7}b-\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{19}+x)(\frac{6}{2}-x)& =(\color{red}{x}+\color{orange}{\frac{12}{19}}).(\color{green}{-x}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{12}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -xx+3x-\frac{12}{19}x+\frac{12}{19}.3& \text{Uitwerken } \\ & =-x^2+(3+(\frac{-12}{19}))x+(\frac{-36}{19}) & \text{Neem samen} \\ &=-x^2+\frac{45}{19}x+(\frac{-36}{19}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{7}+x)(\frac{9}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{-2}{7}}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{4}x+\frac{2}{7}q-\frac{2}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx+\frac{3}{4}x+\frac{2}{7}q-\frac{6}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{3}{4}x+\frac{2}{7}q-\frac{3}{14} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{11}+p)(\frac{-14}{7}+x)& =(\color{red}{p}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-\frac{4}{11}x+\frac{4}{11}.2& \text{Uitwerken } \\ & =px-2p-\frac{4}{11}x+\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-17}{12})(p+\frac{-14}{14})& =(\color{red}{p}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{17}{12}p+\frac{17}{12}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-17}{12}))p+\frac{17}{12} & \text{Neem samen} \\ &=p^2-\frac{29}{12}p+\frac{17}{12} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{14}+a)(\frac{3}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{19}a-\frac{4}{7}q-\frac{4}{7}.\frac{3}{19}& \text{Uitwerken } \\ & =aq+\frac{3}{19}a-\frac{4}{7}q-\frac{12}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{8}+x)(a+\frac{8}{6})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{3}x+1a+1.\frac{4}{3}& \text{Uitwerken } \\ & =ax+\frac{4}{3}x+1a+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-11}{2})(\frac{20}{5}+a)& =(\color{red}{a}+\color{orange}{\frac{11}{2}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aa+4a+\frac{11}{2}a+\frac{11}{2}.4& \text{Uitwerken } \\ & =a^2+(4+\frac{11}{2})a+\frac{44}{2} & \text{Neem samen} \\ &=a^2+\frac{19}{2}a+\frac{44}{2} & \text{Maak de som} \\ &=a^2+\frac{19}{2}a+22 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-10}{15})(\frac{-9}{8}+p)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{8}p+\frac{2}{3}p-\frac{2}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{8})+\frac{2}{3})p-(\frac{-18}{24}) & \text{Neem samen} \\ &=p^2-\frac{11}{24}p-(\frac{-18}{24}) & \text{Maak de som} \\ &=p^2-\frac{11}{24}p+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-15}{13}-b)(a-\frac{16}{6})& =(\color{red}{-b}+\color{orange}{\frac{-15}{13}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{3}b-\frac{15}{13}a+\frac{15}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =-ab+\frac{8}{3}b-\frac{15}{13}a+\frac{120}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{8}{3}b-\frac{15}{13}a+\frac{40}{13} & \text{Vereenvoudig} \\\end{align}\)
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