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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{16}{20}+b)(\frac{-10}{15}+p)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{3}b+\frac{4}{5}p-\frac{4}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =bp-\frac{2}{3}b+\frac{4}{5}p-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{3}{14})(x-\frac{2}{18})& =(\color{red}{p}+\color{orange}{\frac{-3}{14}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{9}p-\frac{3}{14}x+\frac{3}{14}.\frac{1}{9}& \text{Uitwerken } \\ & =px-\frac{1}{9}p-\frac{3}{14}x+\frac{3}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{9}p-\frac{3}{14}x+\frac{1}{42} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-7}{8}-q)(\frac{-3}{2}-a)& =(\color{red}{-q}+\color{orange}{\frac{-7}{8}}).(\color{green}{-a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}q+\frac{7}{8}a+\frac{7}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}q+\frac{7}{8}a+\frac{21}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{8}{14})(x+\frac{-13}{2})& =(\color{red}{b}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{2}b-\frac{4}{7}x+\frac{4}{7}.\frac{13}{2}& \text{Uitwerken } \\ & =bx-\frac{13}{2}b-\frac{4}{7}x+\frac{52}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{13}{2}b-\frac{4}{7}x+\frac{26}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-6}{5})(\frac{-10}{19}-b)& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{-b}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{19}b+\frac{6}{5}b+\frac{6}{5}.\frac{10}{19}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{19})+\frac{6}{5})b+(\frac{-60}{95}) & \text{Neem samen} \\ &=-b^2+\frac{64}{95}b+(\frac{-60}{95}) & \text{Maak de som} \\ &=-b^2+\frac{64}{95}b+(\frac{-12}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-5}{5})(q+\frac{20}{15})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{4}{3}q+1q+1.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+(\frac{4}{3}+1)q+\frac{4}{3} & \text{Neem samen} \\ &=q^2+\frac{7}{3}q+\frac{4}{3} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{9}-q)(\frac{8}{14}+b)& =(\color{red}{-q}+\color{orange}{\frac{-16}{9}}).(\color{green}{b}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{4}{7}q-\frac{16}{9}b-\frac{16}{9}.\frac{4}{7}& \text{Uitwerken } \\ & =-bq-\frac{4}{7}q-\frac{16}{9}b-\frac{64}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{5}{8})(\frac{-16}{11}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{11}p-\frac{5}{8}b+\frac{5}{8}.\frac{16}{11}& \text{Uitwerken } \\ & =bp-\frac{16}{11}p-\frac{5}{8}b+\frac{80}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{11}p-\frac{5}{8}b+\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{18}+p)(b+\frac{-2}{16})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{8}p-\frac{5}{9}b+\frac{5}{9}.\frac{1}{8}& \text{Uitwerken } \\ & =bp-\frac{1}{8}p-\frac{5}{9}b+\frac{5}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{9}{14})(\frac{12}{11}-b)& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{-b}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{9}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{12}{11}p-\frac{9}{14}b+\frac{9}{14}.\frac{12}{11}& \text{Uitwerken } \\ & =-bp+\frac{12}{11}p-\frac{9}{14}b+\frac{108}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{12}{11}p-\frac{9}{14}b+\frac{54}{77} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{12}{12})(b-\frac{16}{4})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bp-4p+1b-1.4& \text{Uitwerken } \\ & =bp-4p+1b-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{13}{13})(\frac{14}{17}+a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{14}{17}b+1a+1.\frac{14}{17}& \text{Uitwerken } \\ & =ab+\frac{14}{17}b+1a+\frac{14}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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