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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{3}{8})(q+\frac{-8}{5})& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{5}x-\frac{3}{8}q+\frac{3}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =qx-\frac{8}{5}x-\frac{3}{8}q+\frac{24}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{8}{5}x-\frac{3}{8}q+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-2}{16}+p)(a-\frac{-4}{3})& =(\color{red}{p}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p-\frac{1}{8}a-\frac{1}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p-\frac{1}{8}a-\frac{4}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{3}p-\frac{1}{8}a-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{4}-a)(\frac{-7}{17}+x)& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{17}a+\frac{3}{2}x-\frac{3}{2}.\frac{7}{17}& \text{Uitwerken } \\ & =-ax+\frac{7}{17}a+\frac{3}{2}x-\frac{21}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{15}-p)(\frac{18}{6}+q)& =(\color{red}{-p}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -pq-3p+\frac{3}{5}q+\frac{3}{5}.3& \text{Uitwerken } \\ & =-pq-3p+\frac{3}{5}q+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{1}{8})(\frac{9}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{-a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{9}{5}a-\frac{1}{8}a+\frac{1}{8}.\frac{9}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{9}{5}+(\frac{-1}{8}))a+(\frac{-9}{40}) & \text{Neem samen} \\ &=-a^2+\frac{67}{40}a+(\frac{-9}{40}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{12}+p)(p+\frac{4}{13})& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{13}p+\frac{1}{6}p+\frac{1}{6}.\frac{4}{13}& \text{Uitwerken } \\ & =p^2+(\frac{4}{13}+\frac{1}{6})p+\frac{4}{78} & \text{Neem samen} \\ &=p^2+\frac{37}{78}p+\frac{4}{78} & \text{Maak de som} \\ &=p^2+\frac{37}{78}p+\frac{2}{39} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{2}-p)(a+\frac{8}{17})& =(\color{red}{-p}+\color{orange}{(-9)}).(\color{green}{a}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(-9)} . \color{green}{(a)} + \color{orange}{(-9)} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{8}{17}p-9a-9.\frac{8}{17}& \text{Uitwerken } \\ & =-ap-\frac{8}{17}p-9a-\frac{72}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{4}{2})(\frac{-2}{2}+b)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+2b-2.1& \text{Uitwerken } \\ & =bx-1x+2b-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{16}+x)(p+\frac{16}{2})& =(\color{red}{x}+\color{orange}{\frac{15}{16}}).(\color{green}{p}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(8)} + \color{orange}{(\frac{15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = px+8x+\frac{15}{16}p+\frac{15}{16}.8& \text{Uitwerken } \\ & =px+8x+\frac{15}{16}p+\frac{120}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+8x+\frac{15}{16}p+\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-18}{6})(b+\frac{7}{19})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{19}q-3b-3.\frac{7}{19}& \text{Uitwerken } \\ & =bq+\frac{7}{19}q-3b-\frac{21}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{8}+x)(q+\frac{-16}{19})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{19}x+\frac{1}{4}q-\frac{1}{4}.\frac{16}{19}& \text{Uitwerken } \\ & =qx-\frac{16}{19}x+\frac{1}{4}q-\frac{16}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{19}x+\frac{1}{4}q-\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{2}{16}-q)(a+\frac{12}{18})& =(\color{red}{-q}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{3}q+\frac{1}{8}a+\frac{1}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq-\frac{2}{3}q+\frac{1}{8}a+\frac{2}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{2}{3}q+\frac{1}{8}a+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
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