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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-11}{8})(\frac{5}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{11}{8}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{11}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{4}b-\frac{11}{8}b+\frac{11}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{4}+(\frac{-11}{8}))b+(\frac{-11}{32}) & \text{Neem samen} \\ &=-b^2-\frac{9}{8}b+(\frac{-11}{32}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b-\frac{-17}{19})(b+\frac{-10}{4})& =(\color{red}{b}+\color{orange}{\frac{17}{19}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{17}{19})} . \color{green}{(b)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{2}b+\frac{17}{19}b-\frac{17}{19}.\frac{5}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{2})+\frac{17}{19})b-(\frac{-85}{38}) & \text{Neem samen} \\ &=b^2-\frac{61}{38}b-(\frac{-85}{38}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{13}+p)(a+\frac{-9}{6})& =(\color{red}{p}+\color{orange}{\frac{-9}{13}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p-\frac{9}{13}a+\frac{9}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p-\frac{9}{13}a+\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{7}-q)(\frac{-19}{13}-b)& =(\color{red}{-q}+\color{orange}{\frac{-10}{7}}).(\color{green}{-b}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{13}q+\frac{10}{7}b+\frac{10}{7}.\frac{19}{13}& \text{Uitwerken } \\ & =bq+\frac{19}{13}q+\frac{10}{7}b+\frac{190}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{-1}{11})(\frac{-18}{13}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{-q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{1}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{18}{13}b-\frac{1}{11}q-\frac{1}{11}.\frac{18}{13}& \text{Uitwerken } \\ & =-bq-\frac{18}{13}b-\frac{1}{11}q-\frac{18}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-10}{7})(\frac{-10}{9}-q)& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{-q}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{9}a+\frac{10}{7}q+\frac{10}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =-aq-\frac{10}{9}a+\frac{10}{7}q+\frac{100}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-8}{16}+q)(q+10)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = qq+10q-\frac{1}{2}q-\frac{1}{2}.10& \text{Uitwerken } \\ & =q^2+(10+(\frac{-1}{2}))q-(\frac{-10}{2}) & \text{Neem samen} \\ &=q^2+\frac{19}{2}q-(\frac{-10}{2}) & \text{Maak de som} \\ &=q^2+\frac{19}{2}q+5 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(x+\frac{-2}{9})(\frac{-11}{13}+b)& =(\color{red}{x}+\color{orange}{\frac{-2}{9}}).(\color{green}{b}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{13}x-\frac{2}{9}b+\frac{2}{9}.\frac{11}{13}& \text{Uitwerken } \\ & =bx-\frac{11}{13}x-\frac{2}{9}b+\frac{22}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-11}{17})(\frac{-8}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{11}{17}}).(\color{green}{x}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{11}{17})} . \color{green}{(x)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{19}b+\frac{11}{17}x-\frac{11}{17}.\frac{8}{19}& \text{Uitwerken } \\ & =bx-\frac{8}{19}b+\frac{11}{17}x-\frac{88}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{20}{10})(\frac{-3}{6}-a)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-2)} . \color{green}{(-a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{2}p+2a+2.\frac{1}{2}& \text{Uitwerken } \\ & =-ap-\frac{1}{2}p+2a+\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{2}p+2a+1 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a-\frac{14}{18})(\frac{-17}{16}-x)& =(\color{red}{a}+\color{orange}{\frac{-7}{9}}).(\color{green}{-x}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{17}{16}a+\frac{7}{9}x+\frac{7}{9}.\frac{17}{16}& \text{Uitwerken } \\ & =-ax-\frac{17}{16}a+\frac{7}{9}x+\frac{119}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{6}{12}-q)(\frac{16}{15}-b)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{15}q-\frac{1}{2}b+\frac{1}{2}.\frac{16}{15}& \text{Uitwerken } \\ & =bq-\frac{16}{15}q-\frac{1}{2}b+\frac{16}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{16}{15}q-\frac{1}{2}b+\frac{8}{15} & \text{Vereenvoudig} \\\end{align}\)