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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-7}{17})(b+\frac{2}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{17}}).(\color{green}{b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{5}p+\frac{7}{17}b+\frac{7}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =bp+\frac{2}{5}p+\frac{7}{17}b+\frac{14}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-13}{13})(\frac{1}{7}-a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{7}q+1a-1.\frac{1}{7}& \text{Uitwerken } \\ & =-aq+\frac{1}{7}q+1a-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+6)(q-\frac{-3}{5})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{5}x+6q+6.\frac{3}{5}& \text{Uitwerken } \\ & =qx+\frac{3}{5}x+6q+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{12}{8})(b+\frac{15}{18})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{6}q+\frac{3}{2}b+\frac{3}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =bq+\frac{5}{6}q+\frac{3}{2}b+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{6}q+\frac{3}{2}b+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{9}{20})(\frac{9}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{-x}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{9}{7}q+\frac{9}{20}x-\frac{9}{20}.\frac{9}{7}& \text{Uitwerken } \\ & =-qx+\frac{9}{7}q+\frac{9}{20}x-\frac{81}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{10}{15})(q-\frac{-7}{2})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{2}q+\frac{2}{3}q+\frac{2}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =q^2+(\frac{7}{2}+\frac{2}{3})q+\frac{14}{6} & \text{Neem samen} \\ &=q^2+\frac{25}{6}q+\frac{14}{6} & \text{Maak de som} \\ &=q^2+\frac{25}{6}q+\frac{7}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}((-17)-a)(\frac{-11}{17}-a)& =(\color{red}{-a}+\color{orange}{(-17)}).(\color{green}{-a}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(-17)} . \color{green}{(-a)} + \color{orange}{(-17)} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{17}a+17a+17.\frac{11}{17}& \text{Uitwerken } \\ & =a^2+(\frac{11}{17}+17)a+\frac{187}{17} & \text{Neem samen} \\ &=a^2+\frac{300}{17}a+\frac{187}{17} & \text{Maak de som} \\ &=a^2+\frac{300}{17}a+11 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{5}+b)(\frac{-16}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{-q}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{16}{9}b+\frac{4}{5}q+\frac{4}{5}.\frac{16}{9}& \text{Uitwerken } \\ & =-bq-\frac{16}{9}b+\frac{4}{5}q+\frac{64}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{10}{16}+a)(\frac{-9}{12}-x)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{-x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{4}a-\frac{5}{8}x-\frac{5}{8}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax-\frac{3}{4}a-\frac{5}{8}x-\frac{15}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-2}{16})(\frac{-15}{14}-x)& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{-x}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{14}b+\frac{1}{8}x+\frac{1}{8}.\frac{15}{14}& \text{Uitwerken } \\ & =-bx-\frac{15}{14}b+\frac{1}{8}x+\frac{15}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{12}{16})(\frac{11}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{2}b-\frac{3}{4}a-\frac{3}{4}.\frac{11}{2}& \text{Uitwerken } \\ & =ab+\frac{11}{2}b-\frac{3}{4}a-\frac{33}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{14}+x)(p-\frac{20}{2})& =(\color{red}{x}+\color{orange}{\frac{-3}{7}}).(\color{green}{p}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-10)} + \color{orange}{(\frac{-3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = px-10x-\frac{3}{7}p+\frac{3}{7}.10& \text{Uitwerken } \\ & =px-10x-\frac{3}{7}p+\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-11 22:43:59
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