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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-5}{2})(\frac{6}{18}-a)& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{-a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{3}q-\frac{5}{2}a+\frac{5}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =-aq+\frac{1}{3}q-\frac{5}{2}a+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{8}-b)(b-\frac{7}{16})& =(\color{red}{-b}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{16}b+\frac{19}{8}b-\frac{19}{8}.\frac{7}{16}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{16}+\frac{19}{8})b-\frac{133}{128} & \text{Neem samen} \\ &=-b^2+\frac{45}{16}b-\frac{133}{128} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{20}{11})(p+\frac{-17}{6})& =(\color{red}{b}+\color{orange}{\frac{20}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{20}{11})} . \color{green}{(p)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{6}b+\frac{20}{11}p-\frac{20}{11}.\frac{17}{6}& \text{Uitwerken } \\ & =bp-\frac{17}{6}b+\frac{20}{11}p-\frac{340}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{17}{6}b+\frac{20}{11}p-\frac{170}{33} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{20}+a)(p-14)& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{p}+\color{blue}{(-14)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-14)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = ap-14a-\frac{1}{5}p+\frac{1}{5}.14& \text{Uitwerken } \\ & =ap-14a-\frac{1}{5}p+\frac{14}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{7}{5})(\frac{-1}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{-a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{6}b-\frac{7}{5}a-\frac{7}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =-ab-\frac{1}{6}b-\frac{7}{5}a-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{8}-b)(\frac{-7}{18}-x)& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{18}b+\frac{1}{2}x+\frac{1}{2}.\frac{7}{18}& \text{Uitwerken } \\ & =bx+\frac{7}{18}b+\frac{1}{2}x+\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{5}+x)(x-\frac{-1}{16})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{16}x+\frac{2}{5}x+\frac{2}{5}.\frac{1}{16}& \text{Uitwerken } \\ & =x^2+(\frac{1}{16}+\frac{2}{5})x+\frac{2}{80} & \text{Neem samen} \\ &=x^2+\frac{37}{80}x+\frac{2}{80} & \text{Maak de som} \\ &=x^2+\frac{37}{80}x+\frac{1}{40} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-3}{10})(\frac{-10}{6}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{3}x+\frac{3}{10}q+\frac{3}{10}.\frac{5}{3}& \text{Uitwerken } \\ & =-qx-\frac{5}{3}x+\frac{3}{10}q+\frac{15}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{5}{3}x+\frac{3}{10}q+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-9}{20}-q)(p-\frac{15}{19})& =(\color{red}{-q}+\color{orange}{\frac{-9}{20}}).(\color{green}{p}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{15}{19}q-\frac{9}{20}p+\frac{9}{20}.\frac{15}{19}& \text{Uitwerken } \\ & =-pq+\frac{15}{19}q-\frac{9}{20}p+\frac{135}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{15}{19}q-\frac{9}{20}p+\frac{27}{76} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{13}+a)(a-\frac{19}{9})& =(\color{red}{a}+\color{orange}{\frac{-4}{13}}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{9}a-\frac{4}{13}a+\frac{4}{13}.\frac{19}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{9})+(\frac{-4}{13}))a+\frac{76}{117} & \text{Neem samen} \\ &=a^2-\frac{283}{117}a+\frac{76}{117} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-9}{4})(\frac{19}{8}+x)& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{x}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{8}a-\frac{9}{4}x-\frac{9}{4}.\frac{19}{8}& \text{Uitwerken } \\ & =ax+\frac{19}{8}a-\frac{9}{4}x-\frac{171}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-7}{18})(q+\frac{10}{6})& =(\color{red}{p}+\color{orange}{\frac{7}{18}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{7}{18})} . \color{green}{(q)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}p+\frac{7}{18}q+\frac{7}{18}.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}p+\frac{7}{18}q+\frac{35}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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