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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{5}+p)(b-\frac{-18}{20})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{10}p-\frac{4}{5}b-\frac{4}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =bp+\frac{9}{10}p-\frac{4}{5}b-\frac{36}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{10}p-\frac{4}{5}b-\frac{18}{25} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x+\frac{15}{10})(\frac{15}{9}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{-p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{3}x-\frac{3}{2}p+\frac{3}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =-px+\frac{5}{3}x-\frac{3}{2}p+\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{3}x-\frac{3}{2}p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-17}{19}+b)(\frac{-18}{4}-q)& =(\color{red}{b}+\color{orange}{\frac{-17}{19}}).(\color{green}{-q}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{2}b+\frac{17}{19}q+\frac{17}{19}.\frac{9}{2}& \text{Uitwerken } \\ & =-bq-\frac{9}{2}b+\frac{17}{19}q+\frac{153}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-6}{10})(\frac{16}{6}+a)& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{3}p-\frac{3}{5}a-\frac{3}{5}.\frac{8}{3}& \text{Uitwerken } \\ & =ap+\frac{8}{3}p-\frac{3}{5}a-\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{8}{3}p-\frac{3}{5}a-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q+\frac{19}{4})(x+\frac{-20}{2})& =(\color{red}{q}+\color{orange}{\frac{19}{4}}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-10)} + \color{orange}{(\frac{19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qx-10q+\frac{19}{4}x-\frac{19}{4}.10& \text{Uitwerken } \\ & =qx-10q+\frac{19}{4}x-\frac{190}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-10q+\frac{19}{4}x-\frac{95}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}((-12)-p)(x-\frac{-1}{3})& =(\color{red}{-p}+\color{orange}{(-12)}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-12)} . \color{green}{(x)} + \color{orange}{(-12)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{3}p-12x-12.\frac{1}{3}& \text{Uitwerken } \\ & =-px-\frac{1}{3}p-12x-\frac{12}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{3}p-12x-4 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-9}{6})(\frac{-9}{8}+b)& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{8}b+\frac{3}{2}b-\frac{3}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{8})+\frac{3}{2})b-(\frac{-27}{16}) & \text{Neem samen} \\ &=b^2+\frac{3}{8}b-(\frac{-27}{16}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{17}{2}-q)(\frac{-2}{16}+a)& =(\color{red}{-q}+\color{orange}{\frac{17}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{17}{2})} . \color{green}{(a)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{8}q+\frac{17}{2}a-\frac{17}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =-aq+\frac{1}{8}q+\frac{17}{2}a-\frac{17}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-6}{14})(\frac{-10}{7}+q)& =(\color{red}{a}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{7}a+\frac{3}{7}q-\frac{3}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =aq-\frac{10}{7}a+\frac{3}{7}q-\frac{30}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{17}-b)(\frac{16}{16}+a)& =(\color{red}{-b}+\color{orange}{\frac{5}{17}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1b+\frac{5}{17}a+\frac{5}{17}.1& \text{Uitwerken } \\ & =-ab-1b+\frac{5}{17}a+\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x+\frac{12}{2})(x+\frac{9}{9})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(6)} . \color{green}{(x)} + \color{orange}{(6)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx+1x+6x+6.1& \text{Uitwerken } \\ & =x^2+(1+6)x+6 & \text{Neem samen} \\ &=x^2+7x+6 & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{11}-a)(\frac{-2}{8}+q)& =(\color{red}{-a}+\color{orange}{\frac{-2}{11}}).(\color{green}{q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{4}a-\frac{2}{11}q+\frac{2}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq+\frac{1}{4}a-\frac{2}{11}q+\frac{2}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{1}{4}a-\frac{2}{11}q+\frac{1}{22} & \text{Vereenvoudig} \\\end{align}\)
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