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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{2}+x)(q-\frac{11}{17})& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{17}x+\frac{3}{2}q-\frac{3}{2}.\frac{11}{17}& \text{Uitwerken } \\ & =qx-\frac{11}{17}x+\frac{3}{2}q-\frac{33}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{20}{13})(\frac{4}{7}+q)& =(\color{red}{a}+\color{orange}{\frac{-20}{13}}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{7}a-\frac{20}{13}q-\frac{20}{13}.\frac{4}{7}& \text{Uitwerken } \\ & =aq+\frac{4}{7}a-\frac{20}{13}q-\frac{80}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{19}{2})(q-\frac{-3}{16})& =(\color{red}{a}+\color{orange}{\frac{19}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{19}{2})} . \color{green}{(q)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{16}a+\frac{19}{2}q+\frac{19}{2}.\frac{3}{16}& \text{Uitwerken } \\ & =aq+\frac{3}{16}a+\frac{19}{2}q+\frac{57}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-4}{5})(a+(-18))& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{(-18)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-18)} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = ax-18x+\frac{4}{5}a-\frac{4}{5}.18& \text{Uitwerken } \\ & =ax-18x+\frac{4}{5}a-\frac{72}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{1}{20})(\frac{-9}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-1}{20}}).(\color{green}{x}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{9}{8}x-\frac{1}{20}x+\frac{1}{20}.\frac{9}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-9}{8})+(\frac{-1}{20}))x+\frac{9}{160} & \text{Neem samen} \\ &=x^2-\frac{47}{40}x+\frac{9}{160} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{18}+a)(\frac{-20}{18}+p)& =(\color{red}{a}+\color{orange}{\frac{11}{18}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{9}a+\frac{11}{18}p-\frac{11}{18}.\frac{10}{9}& \text{Uitwerken } \\ & =ap-\frac{10}{9}a+\frac{11}{18}p-\frac{110}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{10}{9}a+\frac{11}{18}p-\frac{55}{81} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{18}{17}+b)(\frac{3}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{18}{17}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b+\frac{18}{17}x+\frac{18}{17}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b+\frac{18}{17}x+\frac{54}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{4}b+\frac{18}{17}x+\frac{27}{34} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-13}{13})(q+\frac{2}{3})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{2}{3}q-1q-1.\frac{2}{3}& \text{Uitwerken } \\ & =q^2+(\frac{2}{3}+(-1))q-(\frac{-2}{3}) & \text{Neem samen} \\ &=q^2-\frac{1}{3}q-(\frac{-2}{3}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-10}{12})(a-\frac{-19}{4})& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{4}b-\frac{5}{6}a-\frac{5}{6}.\frac{19}{4}& \text{Uitwerken } \\ & =ab+\frac{19}{4}b-\frac{5}{6}a-\frac{95}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{2}{3})(\frac{18}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{2}b+\frac{2}{3}p+\frac{2}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =bp+\frac{9}{2}b+\frac{2}{3}p+\frac{18}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{2}b+\frac{2}{3}p+3 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{2}{2})(q-\frac{15}{4})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{4}q+1q-1.\frac{15}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{4})+1)q-(\frac{-15}{4}) & \text{Neem samen} \\ &=q^2-\frac{11}{4}q-(\frac{-15}{4}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{18}{13})(p+\frac{1}{6})& =(\color{red}{q}+\color{orange}{\frac{18}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{6}q+\frac{18}{13}p+\frac{18}{13}.\frac{1}{6}& \text{Uitwerken } \\ & =pq+\frac{1}{6}q+\frac{18}{13}p+\frac{18}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{6}q+\frac{18}{13}p+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
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