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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-12}{19})(x-\frac{-13}{18})& =(\color{red}{p}+\color{orange}{\frac{-12}{19}}).(\color{green}{x}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{18}p-\frac{12}{19}x-\frac{12}{19}.\frac{13}{18}& \text{Uitwerken } \\ & =px+\frac{13}{18}p-\frac{12}{19}x-\frac{156}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{18}p-\frac{12}{19}x-\frac{26}{57} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{15}-x)(b+\frac{1}{15})& =(\color{red}{-x}+\color{orange}{\frac{-19}{15}}).(\color{green}{b}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{15}x-\frac{19}{15}b-\frac{19}{15}.\frac{1}{15}& \text{Uitwerken } \\ & =-bx-\frac{1}{15}x-\frac{19}{15}b-\frac{19}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{18}-x)(\frac{4}{2}+p)& =(\color{red}{-x}+\color{orange}{\frac{8}{9}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(2)} + \color{orange}{(\frac{8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -px-2x+\frac{8}{9}p+\frac{8}{9}.2& \text{Uitwerken } \\ & =-px-2x+\frac{8}{9}p+\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{4}-q)(\frac{13}{13}+b)& =(\color{red}{-q}+\color{orange}{\frac{11}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{4})} . \color{green}{(b)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1q+\frac{11}{4}b+\frac{11}{4}.1& \text{Uitwerken } \\ & =-bq-1q+\frac{11}{4}b+\frac{11}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-13}{17})(\frac{-18}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{13}{17}}).(\color{green}{q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{13}{17})} . \color{green}{(q)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{17}b+\frac{13}{17}q-\frac{13}{17}.\frac{18}{17}& \text{Uitwerken } \\ & =bq-\frac{18}{17}b+\frac{13}{17}q-\frac{234}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{20}+q)(\frac{10}{2}-x)& =(\color{red}{q}+\color{orange}{\frac{-11}{20}}).(\color{green}{-x}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{-11}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -qx+5q+\frac{11}{20}x-\frac{11}{20}.5& \text{Uitwerken } \\ & =-qx+5q+\frac{11}{20}x-\frac{55}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+5q+\frac{11}{20}x-\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{6}-q)(a+\frac{-14}{14})& =(\color{red}{-q}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q-\frac{1}{6}a+\frac{1}{6}.1& \text{Uitwerken } \\ & =-aq+1q-\frac{1}{6}a+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{7}+p)(\frac{7}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{13}p+\frac{1}{7}b+\frac{1}{7}.\frac{7}{13}& \text{Uitwerken } \\ & =bp+\frac{7}{13}p+\frac{1}{7}b+\frac{7}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{13}p+\frac{1}{7}b+\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-10}{14})(b+(-12))& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{(-12)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-12)} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = bb-12b-\frac{5}{7}b+\frac{5}{7}.12& \text{Uitwerken } \\ & =b^2+((-12)+(\frac{-5}{7}))b+\frac{60}{7} & \text{Neem samen} \\ &=b^2-\frac{89}{7}b+\frac{60}{7} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{9}-a)(\frac{5}{16}-b)& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{16}a-\frac{1}{3}b+\frac{1}{3}.\frac{5}{16}& \text{Uitwerken } \\ & =ab-\frac{5}{16}a-\frac{1}{3}b+\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{20}-b)(q+\frac{13}{7})& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{7}b+\frac{3}{10}q+\frac{3}{10}.\frac{13}{7}& \text{Uitwerken } \\ & =-bq-\frac{13}{7}b+\frac{3}{10}q+\frac{39}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{5}{2})(\frac{-20}{7}-a)& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{-a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{7}a+\frac{5}{2}a+\frac{5}{2}.\frac{20}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{7})+\frac{5}{2})a+(\frac{-100}{14}) & \text{Neem samen} \\ &=-a^2-\frac{5}{14}a+(\frac{-100}{14}) & \text{Maak de som} \\ &=-a^2-\frac{5}{14}a+(\frac{-50}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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