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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{16}{13})(q-\frac{-2}{9})& =(\color{red}{q}+\color{orange}{\frac{16}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{16}{13})} . \color{green}{(q)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{9}q+\frac{16}{13}q+\frac{16}{13}.\frac{2}{9}& \text{Uitwerken } \\ & =q^2+(\frac{2}{9}+\frac{16}{13})q+\frac{32}{117} & \text{Neem samen} \\ &=q^2+\frac{170}{117}q+\frac{32}{117} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b+\frac{13}{9})(a+\frac{-8}{7})& =(\color{red}{b}+\color{orange}{\frac{13}{9}}).(\color{green}{a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{7}b+\frac{13}{9}a-\frac{13}{9}.\frac{8}{7}& \text{Uitwerken } \\ & =ab-\frac{8}{7}b+\frac{13}{9}a-\frac{104}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-10}{15})(a-\frac{-19}{15})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{15}p-\frac{2}{3}a-\frac{2}{3}.\frac{19}{15}& \text{Uitwerken } \\ & =ap+\frac{19}{15}p-\frac{2}{3}a-\frac{38}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{7}{17})(b-\frac{3}{18})& =(\color{red}{q}+\color{orange}{\frac{-7}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{6}q-\frac{7}{17}b+\frac{7}{17}.\frac{1}{6}& \text{Uitwerken } \\ & =bq-\frac{1}{6}q-\frac{7}{17}b+\frac{7}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{10}+a)(\frac{-20}{16}+a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{4}a+1a-1.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{4})+1)a-(\frac{-5}{4}) & \text{Neem samen} \\ &=a^2-\frac{1}{4}a-(\frac{-5}{4}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q+\frac{11}{7})(b-\frac{-9}{8})& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{b}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{11}{7})} . \color{green}{(b)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{8}q+\frac{11}{7}b+\frac{11}{7}.\frac{9}{8}& \text{Uitwerken } \\ & =bq+\frac{9}{8}q+\frac{11}{7}b+\frac{99}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{7}+x)(\frac{-16}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{-18}{7}}).(\color{green}{a}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{11}x-\frac{18}{7}a+\frac{18}{7}.\frac{16}{11}& \text{Uitwerken } \\ & =ax-\frac{16}{11}x-\frac{18}{7}a+\frac{288}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{2}+b)(\frac{4}{10}+a)& =(\color{red}{b}+\color{orange}{\frac{-17}{2}}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{5}b-\frac{17}{2}a-\frac{17}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =ab+\frac{2}{5}b-\frac{17}{2}a-\frac{34}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{5}b-\frac{17}{2}a-\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{16}+b)(q+\frac{3}{8})& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{8}b-\frac{7}{8}q-\frac{7}{8}.\frac{3}{8}& \text{Uitwerken } \\ & =bq+\frac{3}{8}b-\frac{7}{8}q-\frac{21}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-20}{19})(a+\frac{1}{20})& =(\color{red}{p}+\color{orange}{\frac{-20}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{20}p-\frac{20}{19}a-\frac{20}{19}.\frac{1}{20}& \text{Uitwerken } \\ & =ap+\frac{1}{20}p-\frac{20}{19}a-\frac{20}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{20}p-\frac{20}{19}a-\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{2}+b)(a-\frac{19}{18})& =(\color{red}{b}+\color{orange}{\frac{-11}{2}}).(\color{green}{a}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{18}b-\frac{11}{2}a+\frac{11}{2}.\frac{19}{18}& \text{Uitwerken } \\ & =ab-\frac{19}{18}b-\frac{11}{2}a+\frac{209}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-3}{4}+x)(p+\frac{8}{9})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{8}{9}x-\frac{3}{4}p-\frac{3}{4}.\frac{8}{9}& \text{Uitwerken } \\ & =px+\frac{8}{9}x-\frac{3}{4}p-\frac{24}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{8}{9}x-\frac{3}{4}p-\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
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