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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{8}+b)(\frac{-15}{11}+q)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{11}b-1q+1.\frac{15}{11}& \text{Uitwerken } \\ & =bq-\frac{15}{11}b-1q+\frac{15}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{19}{7})(\frac{-19}{10}+b)& =(\color{red}{q}+\color{orange}{\frac{-19}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{10}q-\frac{19}{7}b+\frac{19}{7}.\frac{19}{10}& \text{Uitwerken } \\ & =bq-\frac{19}{10}q-\frac{19}{7}b+\frac{361}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-8}{10})(p-\frac{-10}{15})& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{3}x-\frac{4}{5}p-\frac{4}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =px+\frac{2}{3}x-\frac{4}{5}p-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-11}{11})(q+\frac{-9}{6})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{2}q+1q-1.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{2})+1)q-(\frac{-3}{2}) & \text{Neem samen} \\ &=q^2-\frac{1}{2}q-(\frac{-3}{2}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-11}{15})(b-\frac{-15}{10})& =(\color{red}{a}+\color{orange}{\frac{11}{15}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}a+\frac{11}{15}b+\frac{11}{15}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}a+\frac{11}{15}b+\frac{33}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{2}a+\frac{11}{15}b+\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-7}{14})(a-\frac{-12}{6})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a+\frac{1}{2}a+\frac{1}{2}.2& \text{Uitwerken } \\ & =a^2+(2+\frac{1}{2})a+\frac{2}{2} & \text{Neem samen} \\ &=a^2+\frac{5}{2}a+\frac{2}{2} & \text{Maak de som} \\ &=a^2+\frac{5}{2}a+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{12}{17}+a)(a+\frac{15}{14})& =(\color{red}{a}+\color{orange}{\frac{12}{17}}).(\color{green}{a}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{15}{14}a+\frac{12}{17}a+\frac{12}{17}.\frac{15}{14}& \text{Uitwerken } \\ & =a^2+(\frac{15}{14}+\frac{12}{17})a+\frac{180}{238} & \text{Neem samen} \\ &=a^2+\frac{423}{238}a+\frac{180}{238} & \text{Maak de som} \\ &=a^2+\frac{423}{238}a+\frac{90}{119} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-1}{3})(\frac{17}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{4}p-\frac{1}{3}b-\frac{1}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =bp+\frac{17}{4}p-\frac{1}{3}b-\frac{17}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-12}{7})(p+\frac{-6}{5})& =(\color{red}{x}+\color{orange}{\frac{-12}{7}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{5}x-\frac{12}{7}p+\frac{12}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =px-\frac{6}{5}x-\frac{12}{7}p+\frac{72}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-(-16))(\frac{-19}{4}-a)& =(\color{red}{q}+\color{orange}{16}).(\color{green}{-a}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(16)} . \color{green}{(-a)} + \color{orange}{(16)} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{4}q-16a-16.\frac{19}{4}& \text{Uitwerken } \\ & =-aq-\frac{19}{4}q-16a-\frac{304}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{4}q-16a-76 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{4}{20})(p-\frac{2}{2})& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q+\frac{1}{5}p-\frac{1}{5}.1& \text{Uitwerken } \\ & =pq-1q+\frac{1}{5}p-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-15}{20})(x-\frac{18}{11})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{18}{11}x+\frac{3}{4}x-\frac{3}{4}.\frac{18}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-18}{11})+\frac{3}{4})x-(\frac{-54}{44}) & \text{Neem samen} \\ &=x^2-\frac{39}{44}x-(\frac{-54}{44}) & \text{Maak de som} \\ &=x^2-\frac{39}{44}x+\frac{27}{22} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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