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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{12}-p)(\frac{19}{10}+b)& =(\color{red}{-p}+\color{orange}{\frac{13}{12}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{10}p+\frac{13}{12}b+\frac{13}{12}.\frac{19}{10}& \text{Uitwerken } \\ & =-bp-\frac{19}{10}p+\frac{13}{12}b+\frac{247}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{10}{5}-a)(a-\frac{19}{16})& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{19}{16}a+2a-2.\frac{19}{16}& \text{Uitwerken } \\ & =-a^2+(\frac{19}{16}+2)a-\frac{38}{16} & \text{Neem samen} \\ &=-a^2+\frac{51}{16}a-\frac{38}{16} & \text{Maak de som} \\ &=-a^2+\frac{51}{16}a-\frac{19}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-7}{7})(p+\frac{-18}{14})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{7}x+1p-1.\frac{9}{7}& \text{Uitwerken } \\ & =px-\frac{9}{7}x+1p-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{17}{4})(a+\frac{8}{20})& =(\color{red}{b}+\color{orange}{\frac{-17}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{5}b-\frac{17}{4}a-\frac{17}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =ab+\frac{2}{5}b-\frac{17}{4}a-\frac{34}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{5}b-\frac{17}{4}a-\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{8}+a)(p-\frac{-10}{2})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(5)} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ap+5a-2p-2.5& \text{Uitwerken } \\ & =ap+5a-2p-10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{18}+q)(\frac{-2}{9}-a)& =(\color{red}{q}+\color{orange}{\frac{-10}{9}}).(\color{green}{-a}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{9}q+\frac{10}{9}a+\frac{10}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =-aq-\frac{2}{9}q+\frac{10}{9}a+\frac{20}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{11}{14})(\frac{2}{8}+x)& =(\color{red}{a}+\color{orange}{\frac{11}{14}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}a+\frac{11}{14}x+\frac{11}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}a+\frac{11}{14}x+\frac{11}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-14}{19})(q+\frac{-16}{11})& =(\color{red}{b}+\color{orange}{\frac{14}{19}}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{11}b+\frac{14}{19}q-\frac{14}{19}.\frac{16}{11}& \text{Uitwerken } \\ & =bq-\frac{16}{11}b+\frac{14}{19}q-\frac{224}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-14)+x)(a-\frac{18}{8})& =(\color{red}{x}+\color{orange}{(-14)}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(-14)} . \color{green}{(a)} + \color{orange}{(-14)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{4}x-14a+14.\frac{9}{4}& \text{Uitwerken } \\ & =ax-\frac{9}{4}x-14a+\frac{126}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{4}x-14a+\frac{63}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{14}+a)(\frac{18}{7}+b)& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{b}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{18}{7}a-\frac{8}{7}b-\frac{8}{7}.\frac{18}{7}& \text{Uitwerken } \\ & =ab+\frac{18}{7}a-\frac{8}{7}b-\frac{144}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{3}+p)(\frac{20}{15}+q)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}p+1q+1.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}p+1q+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-17}{9})(p-\frac{18}{2})& =(\color{red}{q}+\color{orange}{\frac{-17}{9}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(\frac{-17}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = pq-9q-\frac{17}{9}p+\frac{17}{9}.9& \text{Uitwerken } \\ & =pq-9q-\frac{17}{9}p+\frac{153}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-9q-\frac{17}{9}p+17 & \text{Vereenvoudig} \\\end{align}\)
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