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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

  1. \((b-\frac{18}{4})(a-\frac{12}{10})\)
  2. \((b+\frac{-10}{17})(\frac{-20}{10}-a)\)
  3. \((p+\frac{-13}{15})(q-\frac{3}{20})\)
  4. \((\frac{18}{20}-x)(\frac{20}{19}+x)\)
  5. \((b-9)(x-\frac{-8}{3})\)
  6. \((\frac{-17}{16}-x)(\frac{15}{17}+p)\)
  7. \((\frac{18}{16}+q)(b+\frac{13}{8})\)
  8. \((\frac{-3}{10}-p)(p+\frac{-4}{16})\)
  9. \((p+\frac{11}{20})(\frac{-6}{13}+q)\)
  10. \((\frac{5}{16}+b)(a-(-4))\)
  11. \((\frac{6}{20}+x)(\frac{1}{9}+q)\)
  12. \((\frac{-17}{10}+q)(p+\frac{-4}{5})\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{18}{4})(a-\frac{12}{10})& =(\color{red}{b}+\color{orange}{\frac{-9}{2}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{5}b-\frac{9}{2}a+\frac{9}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =ab-\frac{6}{5}b-\frac{9}{2}a+\frac{54}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{5}b-\frac{9}{2}a+\frac{27}{5} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-10}{17})(\frac{-20}{10}-a)& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab-2b+\frac{10}{17}a+\frac{10}{17}.2& \text{Uitwerken } \\ & =-ab-2b+\frac{10}{17}a+\frac{20}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-13}{15})(q-\frac{3}{20})& =(\color{red}{p}+\color{orange}{\frac{-13}{15}}).(\color{green}{q}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{20}p-\frac{13}{15}q+\frac{13}{15}.\frac{3}{20}& \text{Uitwerken } \\ & =pq-\frac{3}{20}p-\frac{13}{15}q+\frac{39}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{20}p-\frac{13}{15}q+\frac{13}{100} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{20}-x)(\frac{20}{19}+x)& =(\color{red}{-x}+\color{orange}{\frac{9}{10}}).(\color{green}{x}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{9}{10})} . \color{green}{(x)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{20}{19}x+\frac{9}{10}x+\frac{9}{10}.\frac{20}{19}& \text{Uitwerken } \\ & =-x^2+((\frac{-20}{19})+\frac{9}{10})x+(\frac{-180}{190}) & \text{Neem samen} \\ &=-x^2-\frac{29}{190}x+(\frac{-180}{190}) & \text{Maak de som} \\ &=-x^2-\frac{29}{190}x+(\frac{-18}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b-9)(x-\frac{-8}{3})& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{3}b-9x-9.\frac{8}{3}& \text{Uitwerken } \\ & =bx+\frac{8}{3}b-9x-\frac{72}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{8}{3}b-9x-24 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-17}{16}-x)(\frac{15}{17}+p)& =(\color{red}{-x}+\color{orange}{\frac{-17}{16}}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{15}{17}x-\frac{17}{16}p-\frac{17}{16}.\frac{15}{17}& \text{Uitwerken } \\ & =-px-\frac{15}{17}x-\frac{17}{16}p-\frac{255}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{15}{17}x-\frac{17}{16}p-\frac{15}{16} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{16}+q)(b+\frac{13}{8})& =(\color{red}{q}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{8}q+\frac{9}{8}b+\frac{9}{8}.\frac{13}{8}& \text{Uitwerken } \\ & =bq+\frac{13}{8}q+\frac{9}{8}b+\frac{117}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{10}-p)(p+\frac{-4}{16})& =(\color{red}{-p}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{4}p-\frac{3}{10}p+\frac{3}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{4}+(\frac{-3}{10}))p+(\frac{-3}{40}) & \text{Neem samen} \\ &=-p^2-\frac{1}{20}p+(\frac{-3}{40}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p+\frac{11}{20})(\frac{-6}{13}+q)& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{11}{20})} . \color{green}{(q)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{13}p+\frac{11}{20}q-\frac{11}{20}.\frac{6}{13}& \text{Uitwerken } \\ & =pq-\frac{6}{13}p+\frac{11}{20}q-\frac{66}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{13}p+\frac{11}{20}q-\frac{33}{130} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{5}{16}+b)(a-(-4))& =(\color{red}{b}+\color{orange}{\frac{5}{16}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ab+4b+\frac{5}{16}a+\frac{5}{16}.4& \text{Uitwerken } \\ & =ab+4b+\frac{5}{16}a+\frac{20}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+4b+\frac{5}{16}a+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{6}{20}+x)(\frac{1}{9}+q)& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{9}x+\frac{3}{10}q+\frac{3}{10}.\frac{1}{9}& \text{Uitwerken } \\ & =qx+\frac{1}{9}x+\frac{3}{10}q+\frac{3}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{9}x+\frac{3}{10}q+\frac{1}{30} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{10}+q)(p+\frac{-4}{5})& =(\color{red}{q}+\color{orange}{\frac{-17}{10}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{5}q-\frac{17}{10}p+\frac{17}{10}.\frac{4}{5}& \text{Uitwerken } \\ & =pq-\frac{4}{5}q-\frac{17}{10}p+\frac{68}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{5}q-\frac{17}{10}p+\frac{34}{25} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-31 15:27:34
Een site van Busleyden Atheneum Mechelen