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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{19}-q)(q+\frac{-14}{14})& =(\color{red}{-q}+\color{orange}{\frac{-2}{19}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq+1q-\frac{2}{19}q+\frac{2}{19}.1& \text{Uitwerken } \\ & =-q^2+(1+(\frac{-2}{19}))q+(\frac{-2}{19}) & \text{Neem samen} \\ &=-q^2+\frac{17}{19}q+(\frac{-2}{19}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(q-\frac{-1}{14})(\frac{-17}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{p}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{1}{14})} . \color{green}{(p)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{7}q+\frac{1}{14}p-\frac{1}{14}.\frac{17}{7}& \text{Uitwerken } \\ & =pq-\frac{17}{7}q+\frac{1}{14}p-\frac{17}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-4}{2})(a-\frac{-17}{7})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{7}x+2a+2.\frac{17}{7}& \text{Uitwerken } \\ & =ax+\frac{17}{7}x+2a+\frac{34}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{11}{11}+b)(p-\frac{-1}{9})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{9}b+1p+1.\frac{1}{9}& \text{Uitwerken } \\ & =bp+\frac{1}{9}b+1p+\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-17}{15}+b)(x+\frac{2}{5})& =(\color{red}{b}+\color{orange}{\frac{-17}{15}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{5}b-\frac{17}{15}x-\frac{17}{15}.\frac{2}{5}& \text{Uitwerken } \\ & =bx+\frac{2}{5}b-\frac{17}{15}x-\frac{34}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{9}{18})(\frac{2}{13}-x)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{13}a-\frac{1}{2}x+\frac{1}{2}.\frac{2}{13}& \text{Uitwerken } \\ & =-ax+\frac{2}{13}a-\frac{1}{2}x+\frac{2}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{2}{13}a-\frac{1}{2}x+\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(18-a)(\frac{19}{9}+x)& =(\color{red}{-a}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{9})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{19}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{19}{9}a+18x+18.\frac{19}{9}& \text{Uitwerken } \\ & =-ax-\frac{19}{9}a+18x+\frac{342}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{19}{9}a+18x+38 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{8}-x)(\frac{18}{12}-q)& =(\color{red}{-x}+\color{orange}{\frac{-19}{8}}).(\color{green}{-q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{2}x+\frac{19}{8}q-\frac{19}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =qx-\frac{3}{2}x+\frac{19}{8}q-\frac{57}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-2}{7}-x)(a+\frac{6}{11})& =(\color{red}{-x}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{6}{11}x-\frac{2}{7}a-\frac{2}{7}.\frac{6}{11}& \text{Uitwerken } \\ & =-ax-\frac{6}{11}x-\frac{2}{7}a-\frac{12}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+\frac{-16}{6})(q-\frac{13}{20})& =(\color{red}{b}+\color{orange}{\frac{-8}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{20}b-\frac{8}{3}q+\frac{8}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =bq-\frac{13}{20}b-\frac{8}{3}q+\frac{104}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{20}b-\frac{8}{3}q+\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{14}+p)(x+\frac{1}{5})& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{5}p+\frac{4}{7}x+\frac{4}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =px+\frac{1}{5}p+\frac{4}{7}x+\frac{4}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{2}{9}+q)(x-\frac{-17}{8})& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{8}q+\frac{2}{9}x+\frac{2}{9}.\frac{17}{8}& \text{Uitwerken } \\ & =qx+\frac{17}{8}q+\frac{2}{9}x+\frac{34}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{17}{8}q+\frac{2}{9}x+\frac{17}{36} & \text{Vereenvoudig} \\\end{align}\)