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

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  1. \((\frac{-16}{15}+x)(\frac{-14}{18}+b)\)
  2. \((q+\frac{10}{9})(\frac{20}{12}-x)\)
  3. \(((-20)+b)(x-\frac{3}{7})\)
  4. \((\frac{7}{10}+a)(b+\frac{-19}{11})\)
  5. \((b-(-18))(a-\frac{-10}{20})\)
  6. \((\frac{13}{7}-b)(p+\frac{10}{14})\)
  7. \((p+\frac{15}{16})(p+\frac{-1}{17})\)
  8. \((q+\frac{-2}{5})(q+\frac{-1}{9})\)
  9. \((b+\frac{2}{3})(x-\frac{11}{19})\)
  10. \((a-\frac{6}{14})(\frac{5}{13}+a)\)
  11. \((x-\frac{2}{7})(p-\frac{17}{17})\)
  12. \((a+\frac{9}{8})(\frac{-16}{7}-b)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-16}{15}+x)(\frac{-14}{18}+b)& =(\color{red}{x}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{9}x-\frac{16}{15}b+\frac{16}{15}.\frac{7}{9}& \text{Uitwerken } \\ & =bx-\frac{7}{9}x-\frac{16}{15}b+\frac{112}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{10}{9})(\frac{20}{12}-x)& =(\color{red}{q}+\color{orange}{\frac{10}{9}}).(\color{green}{-x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{3}q-\frac{10}{9}x+\frac{10}{9}.\frac{5}{3}& \text{Uitwerken } \\ & =-qx+\frac{5}{3}q-\frac{10}{9}x+\frac{50}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}((-20)+b)(x-\frac{3}{7})& =(\color{red}{b}+\color{orange}{(-20)}).(\color{green}{x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(-20)} . \color{green}{(x)} + \color{orange}{(-20)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{7}b-20x+20.\frac{3}{7}& \text{Uitwerken } \\ & =bx-\frac{3}{7}b-20x+\frac{60}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{10}+a)(b+\frac{-19}{11})& =(\color{red}{a}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{11}a+\frac{7}{10}b-\frac{7}{10}.\frac{19}{11}& \text{Uitwerken } \\ & =ab-\frac{19}{11}a+\frac{7}{10}b-\frac{133}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-(-18))(a-\frac{-10}{20})& =(\color{red}{b}+\color{orange}{18}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(18)} . \color{green}{(a)} + \color{orange}{(18)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}b+18a+18.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}b+18a+\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{2}b+18a+9 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{13}{7}-b)(p+\frac{10}{14})& =(\color{red}{-b}+\color{orange}{\frac{13}{7}}).(\color{green}{p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{7}b+\frac{13}{7}p+\frac{13}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =-bp-\frac{5}{7}b+\frac{13}{7}p+\frac{65}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{15}{16})(p+\frac{-1}{17})& =(\color{red}{p}+\color{orange}{\frac{15}{16}}).(\color{green}{p}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{17}p+\frac{15}{16}p-\frac{15}{16}.\frac{1}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{17})+\frac{15}{16})p-(\frac{-15}{272}) & \text{Neem samen} \\ &=p^2+\frac{239}{272}p-(\frac{-15}{272}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-2}{5})(q+\frac{-1}{9})& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{9}q-\frac{2}{5}q+\frac{2}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{9})+(\frac{-2}{5}))q+\frac{2}{45} & \text{Neem samen} \\ &=q^2-\frac{23}{45}q+\frac{2}{45} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{2}{3})(x-\frac{11}{19})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{19}b+\frac{2}{3}x-\frac{2}{3}.\frac{11}{19}& \text{Uitwerken } \\ & =bx-\frac{11}{19}b+\frac{2}{3}x-\frac{22}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{6}{14})(\frac{5}{13}+a)& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{13}a-\frac{3}{7}a-\frac{3}{7}.\frac{5}{13}& \text{Uitwerken } \\ & =a^2+(\frac{5}{13}+(\frac{-3}{7}))a-(\frac{-15}{91}) & \text{Neem samen} \\ &=a^2-\frac{4}{91}a-(\frac{-15}{91}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-\frac{2}{7})(p-\frac{17}{17})& =(\color{red}{x}+\color{orange}{\frac{-2}{7}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x-\frac{2}{7}p+\frac{2}{7}.1& \text{Uitwerken } \\ & =px-1x-\frac{2}{7}p+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{9}{8})(\frac{-16}{7}-b)& =(\color{red}{a}+\color{orange}{\frac{9}{8}}).(\color{green}{-b}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{7}a-\frac{9}{8}b-\frac{9}{8}.\frac{16}{7}& \text{Uitwerken } \\ & =-ab-\frac{16}{7}a-\frac{9}{8}b-\frac{144}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{16}{7}a-\frac{9}{8}b-\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
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