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

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

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Verbetersleutel

  1. \(\begin{align}(a-\frac{-2}{5})(\frac{8}{12}+b)& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}a+\frac{2}{5}b+\frac{2}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}a+\frac{2}{5}b+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-7}{4})(a+\frac{1}{6})& =(\color{red}{a}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{6}a+\frac{7}{4}a+\frac{7}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =a^2+(\frac{1}{6}+\frac{7}{4})a+\frac{7}{24} & \text{Neem samen} \\ &=a^2+\frac{23}{12}a+\frac{7}{24} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{20}-q)(\frac{-20}{16}+p)& =(\color{red}{-q}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{4}q+\frac{3}{10}p-\frac{3}{10}.\frac{5}{4}& \text{Uitwerken } \\ & =-pq+\frac{5}{4}q+\frac{3}{10}p-\frac{15}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{4}q+\frac{3}{10}p-\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{18}+x)(x-\frac{-8}{19})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{8}{19}x+\frac{7}{9}x+\frac{7}{9}.\frac{8}{19}& \text{Uitwerken } \\ & =x^2+(\frac{8}{19}+\frac{7}{9})x+\frac{56}{171} & \text{Neem samen} \\ &=x^2+\frac{205}{171}x+\frac{56}{171} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-16}{2})(x+\frac{16}{5})& =(\color{red}{q}+\color{orange}{8}).(\color{green}{x}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(8)} . \color{green}{(x)} + \color{orange}{(8)} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{5}q+8x+8.\frac{16}{5}& \text{Uitwerken } \\ & =qx+\frac{16}{5}q+8x+\frac{128}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{6}-b)(x-\frac{-6}{6})& =(\color{red}{-b}+\color{orange}{\frac{7}{3}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b+\frac{7}{3}x+\frac{7}{3}.1& \text{Uitwerken } \\ & =-bx-1b+\frac{7}{3}x+\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{-14}{20})(a+\frac{-6}{18})& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{3}p-\frac{7}{10}a+\frac{7}{10}.\frac{1}{3}& \text{Uitwerken } \\ & =ap-\frac{1}{3}p-\frac{7}{10}a+\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{15}+b)(\frac{17}{8}+q)& =(\color{red}{b}+\color{orange}{\frac{-16}{15}}).(\color{green}{q}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{8}b-\frac{16}{15}q-\frac{16}{15}.\frac{17}{8}& \text{Uitwerken } \\ & =bq+\frac{17}{8}b-\frac{16}{15}q-\frac{272}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{17}{8}b-\frac{16}{15}q-\frac{34}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-1}{8})(q+\frac{-9}{11})& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{11}x+\frac{1}{8}q-\frac{1}{8}.\frac{9}{11}& \text{Uitwerken } \\ & =qx-\frac{9}{11}x+\frac{1}{8}q-\frac{9}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{9}{14})(\frac{9}{20}+b)& =(\color{red}{p}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{20}p-\frac{9}{14}b-\frac{9}{14}.\frac{9}{20}& \text{Uitwerken } \\ & =bp+\frac{9}{20}p-\frac{9}{14}b-\frac{81}{280} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{4}-a)(\frac{17}{9}+a)& =(\color{red}{-a}+\color{orange}{\frac{15}{4}}).(\color{green}{a}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{15}{4})} . \color{green}{(a)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{17}{9}a+\frac{15}{4}a+\frac{15}{4}.\frac{17}{9}& \text{Uitwerken } \\ & =-a^2+((\frac{-17}{9})+\frac{15}{4})a+(\frac{-255}{36}) & \text{Neem samen} \\ &=-a^2+\frac{67}{36}a+(\frac{-255}{36}) & \text{Maak de som} \\ &=-a^2+\frac{67}{36}a+(\frac{-85}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{12}+x)((-10)+q)& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-10)} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qx-10x+\frac{1}{4}q-\frac{1}{4}.10& \text{Uitwerken } \\ & =qx-10x+\frac{1}{4}q-\frac{10}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-10x+\frac{1}{4}q-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
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