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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{11}+a)(\frac{-15}{11}+b)& =(\color{red}{a}+\color{orange}{\frac{7}{11}}).(\color{green}{b}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{7}{11})} . \color{green}{(b)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{11}a+\frac{7}{11}b-\frac{7}{11}.\frac{15}{11}& \text{Uitwerken } \\ & =ab-\frac{15}{11}a+\frac{7}{11}b-\frac{105}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-11}{3}-x)(x-\frac{9}{6})& =(\color{red}{-x}+\color{orange}{\frac{-11}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{2}x-\frac{11}{3}x+\frac{11}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{2}+(\frac{-11}{3}))x+(\frac{-33}{6}) & \text{Neem samen} \\ &=-x^2-\frac{13}{6}x+(\frac{-33}{6}) & \text{Maak de som} \\ &=-x^2-\frac{13}{6}x+(\frac{-11}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{6}-q)(q-\frac{-19}{13})& =(\color{red}{-q}+\color{orange}{(-3)}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(-3)} . \color{green}{(q)} + \color{orange}{(-3)} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{19}{13}q-3q-3.\frac{19}{13}& \text{Uitwerken } \\ & =-q^2+((\frac{-19}{13})+(-3))q-\frac{57}{13} & \text{Neem samen} \\ &=-q^2-\frac{58}{13}q-\frac{57}{13} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-12}{11}-q)(p+\frac{16}{10})& =(\color{red}{-q}+\color{orange}{\frac{-12}{11}}).(\color{green}{p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{5}q-\frac{12}{11}p-\frac{12}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =-pq-\frac{8}{5}q-\frac{12}{11}p-\frac{96}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{11}-b)(x+\frac{11}{9})& =(\color{red}{-b}+\color{orange}{\frac{5}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{5}{11})} . \color{green}{(x)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{9}b+\frac{5}{11}x+\frac{5}{11}.\frac{11}{9}& \text{Uitwerken } \\ & =-bx-\frac{11}{9}b+\frac{5}{11}x+\frac{55}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{11}{9}b+\frac{5}{11}x+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-17}{2})(x+\frac{15}{12})& =(\color{red}{q}+\color{orange}{\frac{-17}{2}}).(\color{green}{x}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{4}q-\frac{17}{2}x-\frac{17}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =qx+\frac{5}{4}q-\frac{17}{2}x-\frac{85}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{9}+b)(p-\frac{13}{16})& =(\color{red}{b}+\color{orange}{\frac{-14}{9}}).(\color{green}{p}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{16}b-\frac{14}{9}p+\frac{14}{9}.\frac{13}{16}& \text{Uitwerken } \\ & =bp-\frac{13}{16}b-\frac{14}{9}p+\frac{182}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{16}b-\frac{14}{9}p+\frac{91}{72} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{1}{15})(\frac{2}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{1}{15}}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{1}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{4}a-\frac{1}{15}x+\frac{1}{15}.\frac{1}{4}& \text{Uitwerken } \\ & =-ax+\frac{1}{4}a-\frac{1}{15}x+\frac{1}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q-\frac{-10}{18})(q+\frac{2}{8})& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{4}q+\frac{5}{9}q+\frac{5}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =q^2+(\frac{1}{4}+\frac{5}{9})q+\frac{5}{36} & \text{Neem samen} \\ &=q^2+\frac{29}{36}q+\frac{5}{36} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-12}{20})(\frac{4}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{3}{5}b+\frac{3}{5}.1& \text{Uitwerken } \\ & =bq+1q+\frac{3}{5}b+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{4}{18})(\frac{3}{15}-a)& =(\color{red}{p}+\color{orange}{\frac{-2}{9}}).(\color{green}{-a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{5}p+\frac{2}{9}a-\frac{2}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =-ap+\frac{1}{5}p+\frac{2}{9}a-\frac{2}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-1}{11})(11+q)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{q}+\color{blue}{11})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(11)} + \color{orange}{(\frac{1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = bq+11b+\frac{1}{11}q+\frac{1}{11}.11& \text{Uitwerken } \\ & =bq+11b+\frac{1}{11}q+\frac{11}{11} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+11b+\frac{1}{11}q+1 & \text{Vereenvoudig} \\\end{align}\)
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