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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{15}-b)(b-\frac{-3}{3})& =(\color{red}{-b}+\color{orange}{\frac{2}{15}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{15})} . \color{green}{(b)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bb-1b+\frac{2}{15}b+\frac{2}{15}.1& \text{Uitwerken } \\ & =-b^2+((-1)+\frac{2}{15})b+(\frac{-2}{15}) & \text{Neem samen} \\ &=-b^2-\frac{13}{15}b+(\frac{-2}{15}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-12}{16})(a+\frac{-1}{9})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{9}b-\frac{3}{4}a+\frac{3}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =ab-\frac{1}{9}b-\frac{3}{4}a+\frac{3}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{9}b-\frac{3}{4}a+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{19}-q)(\frac{-1}{18}-x)& =(\color{red}{-q}+\color{orange}{\frac{2}{19}}).(\color{green}{-x}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{18}q-\frac{2}{19}x-\frac{2}{19}.\frac{1}{18}& \text{Uitwerken } \\ & =qx+\frac{1}{18}q-\frac{2}{19}x-\frac{2}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{18}q-\frac{2}{19}x-\frac{1}{171} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-15}{20}-p)(\frac{-10}{19}-a)& =(\color{red}{-p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{19}p+\frac{3}{4}a+\frac{3}{4}.\frac{10}{19}& \text{Uitwerken } \\ & =ap+\frac{10}{19}p+\frac{3}{4}a+\frac{30}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{10}{19}p+\frac{3}{4}a+\frac{15}{38} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{20}+q)(b-\frac{-17}{7})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{7}q-\frac{1}{2}b-\frac{1}{2}.\frac{17}{7}& \text{Uitwerken } \\ & =bq+\frac{17}{7}q-\frac{1}{2}b-\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{17}{5})(\frac{-3}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{17}{5}}).(\color{green}{-p}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{3}{19}p-\frac{17}{5}p-\frac{17}{5}.\frac{3}{19}& \text{Uitwerken } \\ & =-p^2+((\frac{-3}{19})+(\frac{-17}{5}))p-\frac{51}{95} & \text{Neem samen} \\ &=-p^2-\frac{338}{95}p-\frac{51}{95} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-11}{19})(b-\frac{-8}{7})& =(\color{red}{b}+\color{orange}{\frac{-11}{19}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{8}{7}b-\frac{11}{19}b-\frac{11}{19}.\frac{8}{7}& \text{Uitwerken } \\ & =b^2+(\frac{8}{7}+(\frac{-11}{19}))b-(\frac{-88}{133}) & \text{Neem samen} \\ &=b^2+\frac{75}{133}b-(\frac{-88}{133}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{7}-q)(\frac{7}{5}+a)& =(\color{red}{-q}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{5}q+\frac{4}{7}a+\frac{4}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =-aq-\frac{7}{5}q+\frac{4}{7}a+\frac{28}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{5}q+\frac{4}{7}a+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{5}{18})(\frac{11}{15}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{a}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{5}{18})} . \color{green}{(a)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{15}x+\frac{5}{18}a+\frac{5}{18}.\frac{11}{15}& \text{Uitwerken } \\ & =ax+\frac{11}{15}x+\frac{5}{18}a+\frac{55}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{15}x+\frac{5}{18}a+\frac{11}{54} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{20}+p)(\frac{15}{19}+b)& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{b}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{15}{19}p-\frac{7}{10}b-\frac{7}{10}.\frac{15}{19}& \text{Uitwerken } \\ & =bp+\frac{15}{19}p-\frac{7}{10}b-\frac{105}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{15}{19}p-\frac{7}{10}b-\frac{21}{38} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{8}+q)(q-\frac{17}{11})& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{17}{11}q-\frac{9}{4}q+\frac{9}{4}.\frac{17}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-17}{11})+(\frac{-9}{4}))q+\frac{153}{44} & \text{Neem samen} \\ &=q^2-\frac{167}{44}q+\frac{153}{44} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-6}{5}+p)(\frac{10}{13}-a)& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{-a}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{13}p+\frac{6}{5}a-\frac{6}{5}.\frac{10}{13}& \text{Uitwerken } \\ & =-ap+\frac{10}{13}p+\frac{6}{5}a-\frac{60}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{10}{13}p+\frac{6}{5}a-\frac{12}{13} & \text{Vereenvoudig} \\\end{align}\)
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