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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{1}{13})(\frac{-4}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a-\frac{1}{13}b-\frac{1}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a-\frac{1}{13}b-\frac{1}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-5}{4})(\frac{13}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{4}p-\frac{5}{4}b-\frac{5}{4}.\frac{13}{4}& \text{Uitwerken } \\ & =bp+\frac{13}{4}p-\frac{5}{4}b-\frac{65}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-20}{10})(x-\frac{18}{13})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{18}{13}x-2x+2.\frac{18}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-18}{13})+(-2))x+\frac{36}{13} & \text{Neem samen} \\ &=x^2-\frac{44}{13}x+\frac{36}{13} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-3}{20})((-16)+x)& =(\color{red}{p}+\color{orange}{\frac{3}{20}}).(\color{green}{x}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-16)} + \color{orange}{(\frac{3}{20})} . \color{green}{(x)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = px-16p+\frac{3}{20}x-\frac{3}{20}.16& \text{Uitwerken } \\ & =px-16p+\frac{3}{20}x-\frac{48}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-16p+\frac{3}{20}x-\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{6}{19})(p-\frac{3}{18})& =(\color{red}{a}+\color{orange}{\frac{6}{19}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{6}{19})} . \color{green}{(p)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{6}a+\frac{6}{19}p-\frac{6}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =ap-\frac{1}{6}a+\frac{6}{19}p-\frac{6}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{6}a+\frac{6}{19}p-\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{7}{17})(\frac{8}{5}-q)& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{-q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{7}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{8}{5}q-\frac{7}{17}q+\frac{7}{17}.\frac{8}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{8}{5}+(\frac{-7}{17}))q+(\frac{-56}{85}) & \text{Neem samen} \\ &=-q^2+\frac{101}{85}q+(\frac{-56}{85}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}((-20)+q)(q-\frac{7}{10})& =(\color{red}{q}+\color{orange}{(-20)}).(\color{green}{q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(-20)} . \color{green}{(q)} + \color{orange}{(-20)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{10}q-20q+20.\frac{7}{10}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{10})+(-20))q+\frac{140}{10} & \text{Neem samen} \\ &=q^2-\frac{207}{10}q+\frac{140}{10} & \text{Maak de som} \\ &=q^2-\frac{207}{10}q+14 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(x-\frac{11}{11})(\frac{7}{17}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{17}x-1b-1.\frac{7}{17}& \text{Uitwerken } \\ & =bx+\frac{7}{17}x-1b-\frac{7}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(14-a)(q+\frac{-3}{20})& =(\color{red}{-a}+\color{orange}{14}).(\color{green}{q}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(14)} . \color{green}{(q)} + \color{orange}{(14)} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{20}a+14q-14.\frac{3}{20}& \text{Uitwerken } \\ & =-aq+\frac{3}{20}a+14q-\frac{42}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{3}{20}a+14q-\frac{21}{10} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{10}+x)(b-\frac{-13}{5})& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{5}x-\frac{7}{10}b-\frac{7}{10}.\frac{13}{5}& \text{Uitwerken } \\ & =bx+\frac{13}{5}x-\frac{7}{10}b-\frac{91}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{6}-q)(11+a)& =(\color{red}{-q}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(11)} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -aq-11q-\frac{7}{3}a-\frac{7}{3}.11& \text{Uitwerken } \\ & =-aq-11q-\frac{7}{3}a-\frac{77}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{4}+x)(\frac{-9}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{10}x-\frac{5}{2}a+\frac{5}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =ax-\frac{9}{10}x-\frac{5}{2}a+\frac{45}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{10}x-\frac{5}{2}a+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
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