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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+17)(\frac{-14}{8}-a)& =(\color{red}{b}+\color{orange}{17}).(\color{green}{-a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(17)} . \color{green}{(-a)} + \color{orange}{(17)} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{4}b-17a-17.\frac{7}{4}& \text{Uitwerken } \\ & =-ab-\frac{7}{4}b-17a-\frac{119}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{19}-a)(\frac{-18}{14}+q)& =(\color{red}{-a}+\color{orange}{\frac{8}{19}}).(\color{green}{q}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{8}{19})} . \color{green}{(q)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{7}a+\frac{8}{19}q-\frac{8}{19}.\frac{9}{7}& \text{Uitwerken } \\ & =-aq+\frac{9}{7}a+\frac{8}{19}q-\frac{72}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{12}{18})(p-\frac{-2}{18})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{9}a+\frac{2}{3}p+\frac{2}{3}.\frac{1}{9}& \text{Uitwerken } \\ & =ap+\frac{1}{9}a+\frac{2}{3}p+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{2}{10})(p-\frac{-5}{11})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{11}b+\frac{1}{5}p+\frac{1}{5}.\frac{5}{11}& \text{Uitwerken } \\ & =bp+\frac{5}{11}b+\frac{1}{5}p+\frac{5}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{11}b+\frac{1}{5}p+\frac{1}{11} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{8}-x)(b+\frac{-18}{7})& =(\color{red}{-x}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{18}{7}x+\frac{5}{2}b-\frac{5}{2}.\frac{18}{7}& \text{Uitwerken } \\ & =-bx+\frac{18}{7}x+\frac{5}{2}b-\frac{90}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{18}{7}x+\frac{5}{2}b-\frac{45}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{19}{16})(\frac{4}{5}-b)& =(\color{red}{b}+\color{orange}{\frac{-19}{16}}).(\color{green}{-b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{4}{5}b+\frac{19}{16}b-\frac{19}{16}.\frac{4}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{4}{5}+\frac{19}{16})b-\frac{76}{80} & \text{Neem samen} \\ &=-b^2+\frac{159}{80}b-\frac{76}{80} & \text{Maak de som} \\ &=-b^2+\frac{159}{80}b-\frac{19}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(a-\frac{2}{19})(b+\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{-2}{19}}).(\color{green}{b}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{5}a-\frac{2}{19}b+\frac{2}{19}.\frac{7}{5}& \text{Uitwerken } \\ & =ab-\frac{7}{5}a-\frac{2}{19}b+\frac{14}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{7}+a)(a+\frac{-1}{12})& =(\color{red}{a}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{12}a+\frac{4}{7}a-\frac{4}{7}.\frac{1}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{12})+\frac{4}{7})a-(\frac{-4}{84}) & \text{Neem samen} \\ &=a^2+\frac{41}{84}a-(\frac{-4}{84}) & \text{Maak de som} \\ &=a^2+\frac{41}{84}a+\frac{1}{21} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{18}-a)(b+\frac{-19}{16})& =(\color{red}{-a}+\color{orange}{\frac{-19}{18}}).(\color{green}{b}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{16}a-\frac{19}{18}b+\frac{19}{18}.\frac{19}{16}& \text{Uitwerken } \\ & =-ab+\frac{19}{16}a-\frac{19}{18}b+\frac{361}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-10}{20})(a+\frac{17}{13})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{13}p-\frac{1}{2}a-\frac{1}{2}.\frac{17}{13}& \text{Uitwerken } \\ & =ap+\frac{17}{13}p-\frac{1}{2}a-\frac{17}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-2}{12})(x+\frac{-3}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{4}b-\frac{1}{6}x+\frac{1}{6}.\frac{1}{4}& \text{Uitwerken } \\ & =bx-\frac{1}{4}b-\frac{1}{6}x+\frac{1}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{13}{15})(\frac{-15}{19}+p)& =(\color{red}{x}+\color{orange}{\frac{13}{15}}).(\color{green}{p}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{15}{19}x+\frac{13}{15}p-\frac{13}{15}.\frac{15}{19}& \text{Uitwerken } \\ & =px-\frac{15}{19}x+\frac{13}{15}p-\frac{195}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{15}{19}x+\frac{13}{15}p-\frac{13}{19} & \text{Vereenvoudig} \\\end{align}\)
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