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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-14}{8})(b+\frac{9}{18})& =(\color{red}{b}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{2}b+\frac{7}{4}b+\frac{7}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+(\frac{1}{2}+\frac{7}{4})b+\frac{7}{8} & \text{Neem samen} \\ &=b^2+\frac{9}{4}b+\frac{7}{8} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-12}{7})(x-\frac{-8}{12})& =(\color{red}{q}+\color{orange}{\frac{-12}{7}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{3}q-\frac{12}{7}x-\frac{12}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =qx+\frac{2}{3}q-\frac{12}{7}x-\frac{24}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{3}q-\frac{12}{7}x-\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-19}{12})(\frac{-18}{17}+x)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{18}{17}p-\frac{19}{12}x+\frac{19}{12}.\frac{18}{17}& \text{Uitwerken } \\ & =px-\frac{18}{17}p-\frac{19}{12}x+\frac{342}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{18}{17}p-\frac{19}{12}x+\frac{57}{34} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{17}{18}-b)(p-\frac{-20}{3})& =(\color{red}{-b}+\color{orange}{\frac{17}{18}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{17}{18})} . \color{green}{(p)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{3}b+\frac{17}{18}p+\frac{17}{18}.\frac{20}{3}& \text{Uitwerken } \\ & =-bp-\frac{20}{3}b+\frac{17}{18}p+\frac{340}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{3}b+\frac{17}{18}p+\frac{170}{27} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{5}+b)(\frac{-18}{14}-x)& =(\color{red}{b}+\color{orange}{\frac{-18}{5}}).(\color{green}{-x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{7}b+\frac{18}{5}x+\frac{18}{5}.\frac{9}{7}& \text{Uitwerken } \\ & =-bx-\frac{9}{7}b+\frac{18}{5}x+\frac{162}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{1}{15})(q+\frac{-8}{2})& =(\color{red}{x}+\color{orange}{\frac{-1}{15}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4x-\frac{1}{15}q+\frac{1}{15}.4& \text{Uitwerken } \\ & =qx-4x-\frac{1}{15}q+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{14}-q)(\frac{3}{20}-a)& =(\color{red}{-q}+\color{orange}{\frac{5}{14}}).(\color{green}{-a}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{5}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{20}q-\frac{5}{14}a+\frac{5}{14}.\frac{3}{20}& \text{Uitwerken } \\ & =aq-\frac{3}{20}q-\frac{5}{14}a+\frac{15}{280} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{20}q-\frac{5}{14}a+\frac{3}{56} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(p-\frac{11}{5})(p+\frac{-11}{3})& =(\color{red}{p}+\color{orange}{\frac{-11}{5}}).(\color{green}{p}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{11}{3}p-\frac{11}{5}p+\frac{11}{5}.\frac{11}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-11}{3})+(\frac{-11}{5}))p+\frac{121}{15} & \text{Neem samen} \\ &=p^2-\frac{88}{15}p+\frac{121}{15} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-13}{17}+a)(\frac{7}{6}-a)& =(\color{red}{a}+\color{orange}{\frac{-13}{17}}).(\color{green}{-a}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{6}a+\frac{13}{17}a-\frac{13}{17}.\frac{7}{6}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{6}+\frac{13}{17})a-\frac{91}{102} & \text{Neem samen} \\ &=-a^2+\frac{197}{102}a-\frac{91}{102} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-18}{20})(b-\frac{2}{8})& =(\color{red}{p}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{4}p-\frac{9}{10}b+\frac{9}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =bp-\frac{1}{4}p-\frac{9}{10}b+\frac{9}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{5}+a)(\frac{1}{6}+p)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{6}a+2p+2.\frac{1}{6}& \text{Uitwerken } \\ & =ap+\frac{1}{6}a+2p+\frac{2}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{6}a+2p+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-13}{14})(x+\frac{-10}{11})& =(\color{red}{b}+\color{orange}{\frac{-13}{14}}).(\color{green}{x}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{11}b-\frac{13}{14}x+\frac{13}{14}.\frac{10}{11}& \text{Uitwerken } \\ & =bx-\frac{10}{11}b-\frac{13}{14}x+\frac{130}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{11}b-\frac{13}{14}x+\frac{65}{77} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-24 04:41:27
Een site van Busleyden Atheneum Mechelen