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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{18}+a)(p-\frac{13}{4})& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{4}a+\frac{5}{6}p-\frac{5}{6}.\frac{13}{4}& \text{Uitwerken } \\ & =ap-\frac{13}{4}a+\frac{5}{6}p-\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-14}{14}+q)(a-\frac{13}{18})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{18}q-1a+1.\frac{13}{18}& \text{Uitwerken } \\ & =aq-\frac{13}{18}q-1a+\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{8}{12}+b)(q-\frac{15}{10})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{2}b+\frac{2}{3}q-\frac{2}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =bq-\frac{3}{2}b+\frac{2}{3}q-\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{2}b+\frac{2}{3}q-1 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{5}{9})(\frac{-14}{17}-x)& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{-x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{14}{17}x+\frac{5}{9}x+\frac{5}{9}.\frac{14}{17}& \text{Uitwerken } \\ & =-x^2+((\frac{-14}{17})+\frac{5}{9})x+(\frac{-70}{153}) & \text{Neem samen} \\ &=-x^2-\frac{41}{153}x+(\frac{-70}{153}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-15}{6})(x-\frac{17}{7})& =(\color{red}{p}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{7}p+\frac{5}{2}x-\frac{5}{2}.\frac{17}{7}& \text{Uitwerken } \\ & =px-\frac{17}{7}p+\frac{5}{2}x-\frac{85}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{10}{9})(a+\frac{20}{16})& =(\color{red}{b}+\color{orange}{\frac{10}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{4}b+\frac{10}{9}a+\frac{10}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =ab+\frac{5}{4}b+\frac{10}{9}a+\frac{50}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{4}b+\frac{10}{9}a+\frac{25}{18} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-13}{16})(\frac{-18}{5}+a)& =(\color{red}{p}+\color{orange}{\frac{13}{16}}).(\color{green}{a}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{5}p+\frac{13}{16}a-\frac{13}{16}.\frac{18}{5}& \text{Uitwerken } \\ & =ap-\frac{18}{5}p+\frac{13}{16}a-\frac{234}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{18}{5}p+\frac{13}{16}a-\frac{117}{40} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}((-7)-p)(\frac{-12}{9}+p)& =(\color{red}{-p}+\color{orange}{(-7)}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-7)} . \color{green}{(p)} + \color{orange}{(-7)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{4}{3}p-7p+7.\frac{4}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{4}{3}+(-7))p+(\frac{-28}{3}) & \text{Neem samen} \\ &=-p^2-\frac{17}{3}p+(\frac{-28}{3}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{3}-b)(\frac{2}{15}-q)& =(\color{red}{-b}+\color{orange}{5}).(\color{green}{-q}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(5)} . \color{green}{(-q)} + \color{orange}{(5)} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{15}b-5q+5.\frac{2}{15}& \text{Uitwerken } \\ & =bq-\frac{2}{15}b-5q+\frac{10}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{2}{15}b-5q+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{5}{17})(a-\frac{-3}{9})& =(\color{red}{b}+\color{orange}{\frac{-5}{17}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}b-\frac{5}{17}a-\frac{5}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}b-\frac{5}{17}a-\frac{5}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{10}{20})(\frac{-4}{20}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{5}b-\frac{1}{2}p+\frac{1}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =bp-\frac{1}{5}b-\frac{1}{2}p+\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-12}{2})(a-\frac{20}{6})& =(\color{red}{q}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{3}q+6a-6.\frac{10}{3}& \text{Uitwerken } \\ & =aq-\frac{10}{3}q+6a-\frac{60}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{10}{3}q+6a-20 & \text{Vereenvoudig} \\\end{align}\)
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