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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-8}{10}+x)(\frac{12}{4}+x)& =(\color{red}{x}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = xx+3x-\frac{4}{5}x-\frac{4}{5}.3& \text{Uitwerken } \\ & =x^2+(3+(\frac{-4}{5}))x-(\frac{-12}{5}) & \text{Neem samen} \\ &=x^2+\frac{11}{5}x-(\frac{-12}{5}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{3}{16}-p)(p-\frac{13}{4})& =(\color{red}{-p}+\color{orange}{\frac{3}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{13}{4}p+\frac{3}{16}p-\frac{3}{16}.\frac{13}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{13}{4}+\frac{3}{16})p-\frac{39}{64} & \text{Neem samen} \\ &=-p^2+\frac{55}{16}p-\frac{39}{64} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{19}{10}-q)(\frac{-18}{10}-x)& =(\color{red}{-q}+\color{orange}{\frac{19}{10}}).(\color{green}{-x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{5}q-\frac{19}{10}x-\frac{19}{10}.\frac{9}{5}& \text{Uitwerken } \\ & =qx+\frac{9}{5}q-\frac{19}{10}x-\frac{171}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{17}{6})(\frac{-19}{10}-x)& =(\color{red}{q}+\color{orange}{\frac{17}{6}}).(\color{green}{-x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{10}q-\frac{17}{6}x-\frac{17}{6}.\frac{19}{10}& \text{Uitwerken } \\ & =-qx-\frac{19}{10}q-\frac{17}{6}x-\frac{323}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-14}{8})(x+\frac{-8}{11})& =(\color{red}{a}+\color{orange}{\frac{7}{4}}).(\color{green}{x}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{7}{4})} . \color{green}{(x)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{11}a+\frac{7}{4}x-\frac{7}{4}.\frac{8}{11}& \text{Uitwerken } \\ & =ax-\frac{8}{11}a+\frac{7}{4}x-\frac{56}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{8}{11}a+\frac{7}{4}x-\frac{14}{11} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{4}-p)(\frac{19}{8}-p)& =(\color{red}{-p}+\color{orange}{\frac{-17}{4}}).(\color{green}{-p}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{8}p+\frac{17}{4}p-\frac{17}{4}.\frac{19}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{8})+\frac{17}{4})p-(\frac{-323}{32}) & \text{Neem samen} \\ &=p^2+\frac{15}{8}p-(\frac{-323}{32}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(p-\frac{1}{13})(\frac{17}{14}+p)& =(\color{red}{p}+\color{orange}{\frac{-1}{13}}).(\color{green}{p}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{14}p-\frac{1}{13}p-\frac{1}{13}.\frac{17}{14}& \text{Uitwerken } \\ & =p^2+(\frac{17}{14}+(\frac{-1}{13}))p-(\frac{-17}{182}) & \text{Neem samen} \\ &=p^2+\frac{207}{182}p-(\frac{-17}{182}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p-\frac{19}{16})(q-\frac{-16}{18})& =(\color{red}{p}+\color{orange}{\frac{-19}{16}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{9}p-\frac{19}{16}q-\frac{19}{16}.\frac{8}{9}& \text{Uitwerken } \\ & =pq+\frac{8}{9}p-\frac{19}{16}q-\frac{152}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{9}p-\frac{19}{16}q-\frac{19}{18} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{15}-a)(\frac{1}{20}-q)& =(\color{red}{-a}+\color{orange}{\frac{-4}{3}}).(\color{green}{-q}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{20}a+\frac{4}{3}q-\frac{4}{3}.\frac{1}{20}& \text{Uitwerken } \\ & =aq-\frac{1}{20}a+\frac{4}{3}q-\frac{4}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{20}a+\frac{4}{3}q-\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-19}{16}+x)(\frac{4}{16}+x)& =(\color{red}{x}+\color{orange}{\frac{-19}{16}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{4}x-\frac{19}{16}x-\frac{19}{16}.\frac{1}{4}& \text{Uitwerken } \\ & =x^2+(\frac{1}{4}+(\frac{-19}{16}))x-(\frac{-19}{64}) & \text{Neem samen} \\ &=x^2-\frac{15}{16}x-(\frac{-19}{64}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(a+\frac{9}{20})(x-\frac{10}{13})& =(\color{red}{a}+\color{orange}{\frac{9}{20}}).(\color{green}{x}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{9}{20})} . \color{green}{(x)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{13}a+\frac{9}{20}x-\frac{9}{20}.\frac{10}{13}& \text{Uitwerken } \\ & =ax-\frac{10}{13}a+\frac{9}{20}x-\frac{90}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{10}{13}a+\frac{9}{20}x-\frac{9}{26} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{8}{10}-p)(b+\frac{-15}{3})& =(\color{red}{-p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-5)} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -bp+5p+\frac{4}{5}b-\frac{4}{5}.5& \text{Uitwerken } \\ & =-bp+5p+\frac{4}{5}b-\frac{20}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+5p+\frac{4}{5}b-4 & \text{Vereenvoudig} \\\end{align}\)