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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{8}{18}+x)(p-\frac{4}{14})& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{7}x+\frac{4}{9}p-\frac{4}{9}.\frac{2}{7}& \text{Uitwerken } \\ & =px-\frac{2}{7}x+\frac{4}{9}p-\frac{8}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{8}+p)(\frac{20}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{-a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{5}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{7}p-\frac{5}{8}a+\frac{5}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =-ap+\frac{10}{7}p-\frac{5}{8}a+\frac{50}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{10}{7}p-\frac{5}{8}a+\frac{25}{28} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-16}{15})(b-\frac{17}{18})& =(\color{red}{b}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{18}b-\frac{16}{15}b+\frac{16}{15}.\frac{17}{18}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{18})+(\frac{-16}{15}))b+\frac{272}{270} & \text{Neem samen} \\ &=b^2-\frac{181}{90}b+\frac{272}{270} & \text{Maak de som} \\ &=b^2-\frac{181}{90}b+\frac{136}{135} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x+\frac{11}{12})(a+\frac{-11}{3})& =(\color{red}{x}+\color{orange}{\frac{11}{12}}).(\color{green}{a}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{11}{12})} . \color{green}{(a)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{3}x+\frac{11}{12}a-\frac{11}{12}.\frac{11}{3}& \text{Uitwerken } \\ & =ax-\frac{11}{3}x+\frac{11}{12}a-\frac{121}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{17}+q)(a-\frac{5}{11})& =(\color{red}{q}+\color{orange}{\frac{-16}{17}}).(\color{green}{a}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{11}q-\frac{16}{17}a+\frac{16}{17}.\frac{5}{11}& \text{Uitwerken } \\ & =aq-\frac{5}{11}q-\frac{16}{17}a+\frac{80}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-4}{2})(a+\frac{2}{3})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}b-2a-2.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}b-2a-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}((-2)+p)(\frac{18}{6}+a)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3p-2a-2.3& \text{Uitwerken } \\ & =ap+3p-2a-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{13}{13})(p-\frac{13}{18})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{18}p+1p-1.\frac{13}{18}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{18})+1)p-(\frac{-13}{18}) & \text{Neem samen} \\ &=p^2+\frac{5}{18}p-(\frac{-13}{18}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-13}{17}+p)(b-\frac{4}{20})& =(\color{red}{p}+\color{orange}{\frac{-13}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{5}p-\frac{13}{17}b+\frac{13}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =bp-\frac{1}{5}p-\frac{13}{17}b+\frac{13}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(17-q)(\frac{13}{10}-a)& =(\color{red}{-q}+\color{orange}{17}).(\color{green}{-a}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(17)} . \color{green}{(-a)} + \color{orange}{(17)} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{10}q-17a+17.\frac{13}{10}& \text{Uitwerken } \\ & =aq-\frac{13}{10}q-17a+\frac{221}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{16}{17})(\frac{10}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{-16}{17}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{4}a+\frac{16}{17}p-\frac{16}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap+\frac{5}{4}a+\frac{16}{17}p-\frac{80}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{5}{4}a+\frac{16}{17}p-\frac{20}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{6}{3}+x)(\frac{9}{2}+x)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{2}x+2x+2.\frac{9}{2}& \text{Uitwerken } \\ & =x^2+(\frac{9}{2}+2)x+\frac{18}{2} & \text{Neem samen} \\ &=x^2+\frac{13}{2}x+\frac{18}{2} & \text{Maak de som} \\ &=x^2+\frac{13}{2}x+9 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-17 05:32:10
Een site van Busleyden Atheneum Mechelen