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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{7}{14})(p+\frac{-18}{16})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{8}b-\frac{1}{2}p+\frac{1}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =bp-\frac{9}{8}b-\frac{1}{2}p+\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{5}{14})(b-\frac{1}{6})& =(\color{red}{a}+\color{orange}{\frac{-5}{14}}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{6}a-\frac{5}{14}b+\frac{5}{14}.\frac{1}{6}& \text{Uitwerken } \\ & =ab-\frac{1}{6}a-\frac{5}{14}b+\frac{5}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{18}+a)(\frac{-9}{14}+p)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{14}a-\frac{1}{2}p+\frac{1}{2}.\frac{9}{14}& \text{Uitwerken } \\ & =ap-\frac{9}{14}a-\frac{1}{2}p+\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{17}+p)(\frac{10}{11}-q)& =(\color{red}{p}+\color{orange}{\frac{14}{17}}).(\color{green}{-q}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{14}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{10}{11}p-\frac{14}{17}q+\frac{14}{17}.\frac{10}{11}& \text{Uitwerken } \\ & =-pq+\frac{10}{11}p-\frac{14}{17}q+\frac{140}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{4}+a)(p-\frac{16}{13})& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{13}a-\frac{3}{4}p+\frac{3}{4}.\frac{16}{13}& \text{Uitwerken } \\ & =ap-\frac{16}{13}a-\frac{3}{4}p+\frac{48}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{16}{13}a-\frac{3}{4}p+\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{-13}{16})(\frac{-16}{6}-b)& =(\color{red}{b}+\color{orange}{\frac{13}{16}}).(\color{green}{-b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{13}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{8}{3}b-\frac{13}{16}b-\frac{13}{16}.\frac{8}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-8}{3})+(\frac{-13}{16}))b-\frac{104}{48} & \text{Neem samen} \\ &=-b^2-\frac{167}{48}b-\frac{104}{48} & \text{Maak de som} \\ &=-b^2-\frac{167}{48}b-\frac{13}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{20}+q)(\frac{-2}{17}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{10}}).(\color{green}{a}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{17}q+\frac{1}{10}a-\frac{1}{10}.\frac{2}{17}& \text{Uitwerken } \\ & =aq-\frac{2}{17}q+\frac{1}{10}a-\frac{2}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{17}q+\frac{1}{10}a-\frac{1}{85} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-2}{2}+q)(\frac{5}{13}-b)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{13}q+1b-1.\frac{5}{13}& \text{Uitwerken } \\ & =-bq+\frac{5}{13}q+1b-\frac{5}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{3}{3})(p-\frac{18}{17})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{17}b+1p-1.\frac{18}{17}& \text{Uitwerken } \\ & =bp-\frac{18}{17}b+1p-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{2}+a)(\frac{7}{9}+x)& =(\color{red}{a}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{9}a-\frac{9}{2}x-\frac{9}{2}.\frac{7}{9}& \text{Uitwerken } \\ & =ax+\frac{7}{9}a-\frac{9}{2}x-\frac{63}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{7}{9}a-\frac{9}{2}x-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{3}{20})(\frac{4}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{3}{20}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pp+1p+\frac{3}{20}p+\frac{3}{20}.1& \text{Uitwerken } \\ & =p^2+(1+\frac{3}{20})p+\frac{3}{20} & \text{Neem samen} \\ &=p^2+\frac{23}{20}p+\frac{3}{20} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}((-10)-p)(x+\frac{-6}{9})& =(\color{red}{-p}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{3}p-10x+10.\frac{2}{3}& \text{Uitwerken } \\ & =-px+\frac{2}{3}p-10x+\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-11 07:20:31
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