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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-15}{16})(x+\frac{17}{8})& =(\color{red}{p}+\color{orange}{\frac{15}{16}}).(\color{green}{x}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{15}{16})} . \color{green}{(x)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{8}p+\frac{15}{16}x+\frac{15}{16}.\frac{17}{8}& \text{Uitwerken } \\ & =px+\frac{17}{8}p+\frac{15}{16}x+\frac{255}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{1}{5})(\frac{16}{5}+b)& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{5}b-\frac{1}{5}b-\frac{1}{5}.\frac{16}{5}& \text{Uitwerken } \\ & =b^2+(\frac{16}{5}+(\frac{-1}{5}))b-(\frac{-16}{25}) & \text{Neem samen} \\ &=b^2+\frac{15}{5}b-(\frac{-16}{25}) & \text{Maak de som} \\ &=b^2+3b+\frac{16}{25} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(p+\frac{1}{8})(\frac{1}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{-x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{3}p-\frac{1}{8}x+\frac{1}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-px+\frac{1}{3}p-\frac{1}{8}x+\frac{1}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{12}-a)(x+\frac{-6}{5})& =(\color{red}{-a}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{6}{5}a+\frac{5}{4}x-\frac{5}{4}.\frac{6}{5}& \text{Uitwerken } \\ & =-ax+\frac{6}{5}a+\frac{5}{4}x-\frac{30}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{6}{5}a+\frac{5}{4}x-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-16}{20})(b-\frac{19}{10})& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{10}q+\frac{4}{5}b-\frac{4}{5}.\frac{19}{10}& \text{Uitwerken } \\ & =bq-\frac{19}{10}q+\frac{4}{5}b-\frac{76}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{10}q+\frac{4}{5}b-\frac{38}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{14}+x)(\frac{3}{8}-b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{8}x+1b-1.\frac{3}{8}& \text{Uitwerken } \\ & =-bx+\frac{3}{8}x+1b-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{10}+p)(q-\frac{10}{4})& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{19}{10})} . \color{green}{(q)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{2}p+\frac{19}{10}q-\frac{19}{10}.\frac{5}{2}& \text{Uitwerken } \\ & =pq-\frac{5}{2}p+\frac{19}{10}q-\frac{95}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{2}p+\frac{19}{10}q-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-(-8))(x+13)& =(\color{red}{b}+\color{orange}{8}).(\color{green}{x}+\color{blue}{13})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(13)} + \color{orange}{(8)} . \color{green}{(x)} + \color{orange}{(8)} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = bx+13b+8x+8.13& \text{Uitwerken } \\ & =bx+13b+8x+104 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-6}{15})(x-\frac{10}{19})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{19}p+\frac{2}{5}x-\frac{2}{5}.\frac{10}{19}& \text{Uitwerken } \\ & =px-\frac{10}{19}p+\frac{2}{5}x-\frac{20}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{19}p+\frac{2}{5}x-\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-19}{17})(a-\frac{14}{8})& =(\color{red}{x}+\color{orange}{\frac{19}{17}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{19}{17})} . \color{green}{(a)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}x+\frac{19}{17}a-\frac{19}{17}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}x+\frac{19}{17}a-\frac{133}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{9}-x)(q+\frac{-2}{6})& =(\color{red}{-x}+\color{orange}{\frac{5}{9}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{3}x+\frac{5}{9}q-\frac{5}{9}.\frac{1}{3}& \text{Uitwerken } \\ & =-qx+\frac{1}{3}x+\frac{5}{9}q-\frac{5}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{8}{15})(b+\frac{-18}{17})& =(\color{red}{q}+\color{orange}{\frac{-8}{15}}).(\color{green}{b}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{17}q-\frac{8}{15}b+\frac{8}{15}.\frac{18}{17}& \text{Uitwerken } \\ & =bq-\frac{18}{17}q-\frac{8}{15}b+\frac{144}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{18}{17}q-\frac{8}{15}b+\frac{48}{85} & \text{Vereenvoudig} \\\end{align}\)
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