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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{18}-a)(\frac{15}{18}+b)& =(\color{red}{-a}+\color{orange}{\frac{7}{18}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{6}a+\frac{7}{18}b+\frac{7}{18}.\frac{5}{6}& \text{Uitwerken } \\ & =-ab-\frac{5}{6}a+\frac{7}{18}b+\frac{35}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-14}{5})(a+\frac{11}{15})& =(\color{red}{q}+\color{orange}{\frac{-14}{5}}).(\color{green}{a}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{15}q-\frac{14}{5}a-\frac{14}{5}.\frac{11}{15}& \text{Uitwerken } \\ & =aq+\frac{11}{15}q-\frac{14}{5}a-\frac{154}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{6}+b)(\frac{15}{11}-x)& =(\color{red}{b}+\color{orange}{\frac{17}{6}}).(\color{green}{-x}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{11}b-\frac{17}{6}x+\frac{17}{6}.\frac{15}{11}& \text{Uitwerken } \\ & =-bx+\frac{15}{11}b-\frac{17}{6}x+\frac{255}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{15}{11}b-\frac{17}{6}x+\frac{85}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{12}{12})(b-\frac{-20}{12})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{3}p-1b-1.\frac{5}{3}& \text{Uitwerken } \\ & =bp+\frac{5}{3}p-1b-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-10}{2})(a-\frac{3}{2})& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}q-5a+5.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}q-5a+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{7}-b)(\frac{7}{9}-q)& =(\color{red}{-b}+\color{orange}{\frac{10}{7}}).(\color{green}{-q}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{9}b-\frac{10}{7}q+\frac{10}{7}.\frac{7}{9}& \text{Uitwerken } \\ & =bq-\frac{7}{9}b-\frac{10}{7}q+\frac{70}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{7}{9}b-\frac{10}{7}q+\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{2}+b)(\frac{-14}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{19}b+\frac{5}{2}x-\frac{5}{2}.\frac{14}{19}& \text{Uitwerken } \\ & =bx-\frac{14}{19}b+\frac{5}{2}x-\frac{70}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{14}{19}b+\frac{5}{2}x-\frac{35}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{9}{18})(p+\frac{-16}{3})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{3}b+\frac{1}{2}p-\frac{1}{2}.\frac{16}{3}& \text{Uitwerken } \\ & =bp-\frac{16}{3}b+\frac{1}{2}p-\frac{16}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{16}{3}b+\frac{1}{2}p-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{4}{7})(a+\frac{18}{14})& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{7}p+\frac{4}{7}a+\frac{4}{7}.\frac{9}{7}& \text{Uitwerken } \\ & =ap+\frac{9}{7}p+\frac{4}{7}a+\frac{36}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{15}+p)(q-2)& =(\color{red}{p}+\color{orange}{\frac{-19}{15}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p-\frac{19}{15}q+\frac{19}{15}.2& \text{Uitwerken } \\ & =pq-2p-\frac{19}{15}q+\frac{38}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{18}{2})(q-\frac{15}{15})& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q-9q+9.1& \text{Uitwerken } \\ & =q^2+((-1)+(-9))q+9 & \text{Neem samen} \\ &=q^2-10q+9 & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{13}+x)(\frac{-15}{20}+a)& =(\color{red}{x}+\color{orange}{\frac{-12}{13}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{4}x-\frac{12}{13}a+\frac{12}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =ax-\frac{3}{4}x-\frac{12}{13}a+\frac{36}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{4}x-\frac{12}{13}a+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
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