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

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Werk uit en vereenvoudig

  1. \((\frac{-14}{14}-x)(a+\frac{-1}{18})\)
  2. \((a+\frac{-7}{19})(b-\frac{-12}{20})\)
  3. \((p+2)(a+\frac{-5}{5})\)
  4. \((x-\frac{-9}{16})(\frac{6}{13}-x)\)
  5. \((\frac{5}{17}-a)(p-\frac{-11}{12})\)
  6. \((b+\frac{7}{19})(\frac{-9}{20}+b)\)
  7. \((\frac{4}{13}-x)(b-\frac{-10}{7})\)
  8. \((a-\frac{-11}{13})(a-\frac{-5}{9})\)
  9. \((\frac{10}{18}+q)(\frac{2}{4}-p)\)
  10. \((p-\frac{-2}{5})(\frac{-4}{8}-q)\)
  11. \((x+\frac{-6}{18})(q+\frac{12}{11})\)
  12. \((\frac{-2}{17}+b)(\frac{2}{2}-p)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-14}{14}-x)(a+\frac{-1}{18})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{18}x-1a+1.\frac{1}{18}& \text{Uitwerken } \\ & =-ax+\frac{1}{18}x-1a+\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-7}{19})(b-\frac{-12}{20})& =(\color{red}{a}+\color{orange}{\frac{-7}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{5}a-\frac{7}{19}b-\frac{7}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =ab+\frac{3}{5}a-\frac{7}{19}b-\frac{21}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+2)(a+\frac{-5}{5})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p+2a-2.1& \text{Uitwerken } \\ & =ap-1p+2a-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-9}{16})(\frac{6}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{-x}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{9}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{6}{13}x-\frac{9}{16}x+\frac{9}{16}.\frac{6}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{6}{13}+(\frac{-9}{16}))x+(\frac{-54}{208}) & \text{Neem samen} \\ &=-x^2-\frac{21}{208}x+(\frac{-54}{208}) & \text{Maak de som} \\ &=-x^2-\frac{21}{208}x+(\frac{-27}{104}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{17}-a)(p-\frac{-11}{12})& =(\color{red}{-a}+\color{orange}{\frac{5}{17}}).(\color{green}{p}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{12}a+\frac{5}{17}p+\frac{5}{17}.\frac{11}{12}& \text{Uitwerken } \\ & =-ap-\frac{11}{12}a+\frac{5}{17}p+\frac{55}{204} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{7}{19})(\frac{-9}{20}+b)& =(\color{red}{b}+\color{orange}{\frac{7}{19}}).(\color{green}{b}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{20}b+\frac{7}{19}b-\frac{7}{19}.\frac{9}{20}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{20})+\frac{7}{19})b-(\frac{-63}{380}) & \text{Neem samen} \\ &=b^2-\frac{31}{380}b-(\frac{-63}{380}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{13}-x)(b-\frac{-10}{7})& =(\color{red}{-x}+\color{orange}{\frac{4}{13}}).(\color{green}{b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{7}x+\frac{4}{13}b+\frac{4}{13}.\frac{10}{7}& \text{Uitwerken } \\ & =-bx-\frac{10}{7}x+\frac{4}{13}b+\frac{40}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-11}{13})(a-\frac{-5}{9})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{9}a+\frac{11}{13}a+\frac{11}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =a^2+(\frac{5}{9}+\frac{11}{13})a+\frac{55}{117} & \text{Neem samen} \\ &=a^2+\frac{164}{117}a+\frac{55}{117} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{18}+q)(\frac{2}{4}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{5}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{2}q-\frac{5}{9}p+\frac{5}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq+\frac{1}{2}q-\frac{5}{9}p+\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-2}{5})(\frac{-4}{8}-q)& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}p-\frac{2}{5}q-\frac{2}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}p-\frac{2}{5}q-\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{2}p-\frac{2}{5}q-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-6}{18})(q+\frac{12}{11})& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{11}x-\frac{1}{3}q-\frac{1}{3}.\frac{12}{11}& \text{Uitwerken } \\ & =qx+\frac{12}{11}x-\frac{1}{3}q-\frac{12}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{11}x-\frac{1}{3}q-\frac{4}{11} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{17}+b)(\frac{2}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{-2}{17}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b+\frac{2}{17}p-\frac{2}{17}.1& \text{Uitwerken } \\ & =-bp+1b+\frac{2}{17}p-\frac{2}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-29 11:21:51
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