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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{4}{5})(\frac{-10}{9}+x)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{9}b+\frac{4}{5}x-\frac{4}{5}.\frac{10}{9}& \text{Uitwerken } \\ & =bx-\frac{10}{9}b+\frac{4}{5}x-\frac{40}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{9}b+\frac{4}{5}x-\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{1}{19}-x)(\frac{-8}{12}-x)& =(\color{red}{-x}+\color{orange}{\frac{1}{19}}).(\color{green}{-x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{3}x-\frac{1}{19}x-\frac{1}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =x^2+(\frac{2}{3}+(\frac{-1}{19}))x-(\frac{-2}{57}) & \text{Neem samen} \\ &=x^2+\frac{35}{57}x-(\frac{-2}{57}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-15}{6})(p-\frac{-11}{15})& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{15}b-\frac{5}{2}p-\frac{5}{2}.\frac{11}{15}& \text{Uitwerken } \\ & =bp+\frac{11}{15}b-\frac{5}{2}p-\frac{55}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{11}{15}b-\frac{5}{2}p-\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{7}{14})(q+\frac{-8}{4})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qq-2q-\frac{1}{2}q+\frac{1}{2}.2& \text{Uitwerken } \\ & =q^2+((-2)+(\frac{-1}{2}))q+\frac{2}{2} & \text{Neem samen} \\ &=q^2-\frac{5}{2}q+\frac{2}{2} & \text{Maak de som} \\ &=q^2-\frac{5}{2}q+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{1}{2}+q)(\frac{6}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{13}q+\frac{1}{2}a+\frac{1}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =aq+\frac{6}{13}q+\frac{1}{2}a+\frac{6}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{6}{13}q+\frac{1}{2}a+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{19}{3})(q+\frac{-4}{16})& =(\color{red}{a}+\color{orange}{\frac{-19}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{4}a-\frac{19}{3}q+\frac{19}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =aq-\frac{1}{4}a-\frac{19}{3}q+\frac{19}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{8}-x)(\frac{2}{10}+p)& =(\color{red}{-x}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{5}x-\frac{1}{4}p-\frac{1}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =-px-\frac{1}{5}x-\frac{1}{4}p-\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(12+b)(\frac{-10}{15}-b)& =(\color{red}{b}+\color{orange}{12}).(\color{green}{-b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(12)} . \color{green}{(-b)} + \color{orange}{(12)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{2}{3}b-12b-12.\frac{2}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-2}{3})+(-12))b-\frac{24}{3} & \text{Neem samen} \\ &=-b^2-\frac{38}{3}b-\frac{24}{3} & \text{Maak de som} \\ &=-b^2-\frac{38}{3}b-8 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{15}+b)(a+\frac{-4}{5})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{5}b+\frac{1}{5}a-\frac{1}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =ab-\frac{4}{5}b+\frac{1}{5}a-\frac{4}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{14}+x)(\frac{15}{16}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{-q}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{16}x+\frac{1}{7}q-\frac{1}{7}.\frac{15}{16}& \text{Uitwerken } \\ & =-qx+\frac{15}{16}x+\frac{1}{7}q-\frac{15}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{11}-x)(q+\frac{-7}{10})& =(\color{red}{-x}+\color{orange}{\frac{5}{11}}).(\color{green}{q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{10}x+\frac{5}{11}q-\frac{5}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =-qx+\frac{7}{10}x+\frac{5}{11}q-\frac{35}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{7}{10}x+\frac{5}{11}q-\frac{7}{22} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-1}{3})(q-\frac{5}{16})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{16}q+\frac{1}{3}q-\frac{1}{3}.\frac{5}{16}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{16})+\frac{1}{3})q-(\frac{-5}{48}) & \text{Neem samen} \\ &=q^2+\frac{1}{48}q-(\frac{-5}{48}) & \text{Maak de som} \\\end{align}\)
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