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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{18}{7})(\frac{20}{7}-x)& =(\color{red}{p}+\color{orange}{\frac{18}{7}}).(\color{green}{-x}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{18}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{20}{7}p-\frac{18}{7}x+\frac{18}{7}.\frac{20}{7}& \text{Uitwerken } \\ & =-px+\frac{20}{7}p-\frac{18}{7}x+\frac{360}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(19-b)(\frac{-3}{3}-a)& =(\color{red}{-b}+\color{orange}{19}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(19)} . \color{green}{(-a)} + \color{orange}{(19)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b-19a-19.1& \text{Uitwerken } \\ & =ab+1b-19a-19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{7}+p)(\frac{15}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{4}p+\frac{6}{7}p+\frac{6}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =p^2+(\frac{5}{4}+\frac{6}{7})p+\frac{30}{28} & \text{Neem samen} \\ &=p^2+\frac{59}{28}p+\frac{30}{28} & \text{Maak de som} \\ &=p^2+\frac{59}{28}p+\frac{15}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(p-\frac{10}{6})(\frac{-9}{5}+x)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{5}p-\frac{5}{3}x+\frac{5}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =px-\frac{9}{5}p-\frac{5}{3}x+\frac{45}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{5}p-\frac{5}{3}x+3 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{14}{9})(\frac{-5}{20}-a)& =(\color{red}{p}+\color{orange}{\frac{14}{9}}).(\color{green}{-a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{14}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{4}p-\frac{14}{9}a-\frac{14}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-ap-\frac{1}{4}p-\frac{14}{9}a-\frac{14}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{4}p-\frac{14}{9}a-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-19}{11})(\frac{-8}{15}-x)& =(\color{red}{b}+\color{orange}{\frac{19}{11}}).(\color{green}{-x}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{15}b-\frac{19}{11}x-\frac{19}{11}.\frac{8}{15}& \text{Uitwerken } \\ & =-bx-\frac{8}{15}b-\frac{19}{11}x-\frac{152}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-18}{3})(a-\frac{-12}{2})& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = aa+6a-6a-6.6& \text{Uitwerken } \\ & =a^2+(6+(-6))a-(-36) & \text{Neem samen} \\ &=a^2+0a-(-36) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+\frac{7}{5})(a+\frac{-15}{16})& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{a}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{15}{16}a+\frac{7}{5}a-\frac{7}{5}.\frac{15}{16}& \text{Uitwerken } \\ & =a^2+((\frac{-15}{16})+\frac{7}{5})a-(\frac{-105}{80}) & \text{Neem samen} \\ &=a^2+\frac{37}{80}a-(\frac{-105}{80}) & \text{Maak de som} \\ &=a^2+\frac{37}{80}a+\frac{21}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-5}{17})(x+\frac{7}{20})& =(\color{red}{x}+\color{orange}{\frac{5}{17}}).(\color{green}{x}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{20}x+\frac{5}{17}x+\frac{5}{17}.\frac{7}{20}& \text{Uitwerken } \\ & =x^2+(\frac{7}{20}+\frac{5}{17})x+\frac{35}{340} & \text{Neem samen} \\ &=x^2+\frac{219}{340}x+\frac{35}{340} & \text{Maak de som} \\ &=x^2+\frac{219}{340}x+\frac{7}{68} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(x-\frac{1}{11})(b+\frac{-1}{8})& =(\color{red}{x}+\color{orange}{\frac{-1}{11}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{8}x-\frac{1}{11}b+\frac{1}{11}.\frac{1}{8}& \text{Uitwerken } \\ & =bx-\frac{1}{8}x-\frac{1}{11}b+\frac{1}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{20}+x)(q+\frac{1}{20})& =(\color{red}{x}+\color{orange}{\frac{3}{20}}).(\color{green}{q}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{3}{20})} . \color{green}{(q)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{20}x+\frac{3}{20}q+\frac{3}{20}.\frac{1}{20}& \text{Uitwerken } \\ & =qx+\frac{1}{20}x+\frac{3}{20}q+\frac{3}{400} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{5}+a)(p-\frac{-12}{3})& =(\color{red}{a}+\color{orange}{\frac{-18}{5}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-18}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4a-\frac{18}{5}p-\frac{18}{5}.4& \text{Uitwerken } \\ & =ap+4a-\frac{18}{5}p-\frac{72}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-30 17:40:08
Een site van Busleyden Atheneum Mechelen