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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{6}{17})(\frac{-9}{4}-p)& =(\color{red}{q}+\color{orange}{\frac{-6}{17}}).(\color{green}{-p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{4}q+\frac{6}{17}p+\frac{6}{17}.\frac{9}{4}& \text{Uitwerken } \\ & =-pq-\frac{9}{4}q+\frac{6}{17}p+\frac{54}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{9}{4}q+\frac{6}{17}p+\frac{27}{34} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{20}{18}-b)(p+\frac{3}{15})& =(\color{red}{-b}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{5}b+\frac{10}{9}p+\frac{10}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp-\frac{1}{5}b+\frac{10}{9}p+\frac{10}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{5}b+\frac{10}{9}p+\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{10}{9})(q+\frac{20}{17})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{q}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{17}x-\frac{10}{9}q-\frac{10}{9}.\frac{20}{17}& \text{Uitwerken } \\ & =qx+\frac{20}{17}x-\frac{10}{9}q-\frac{200}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{6}{5}-q)(\frac{-1}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{6}{5}}).(\color{green}{-b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{9}q-\frac{6}{5}b-\frac{6}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =bq+\frac{1}{9}q-\frac{6}{5}b-\frac{6}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{9}q-\frac{6}{5}b-\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{7}{7}-q)(\frac{7}{13}-b)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{13}q-1b+1.\frac{7}{13}& \text{Uitwerken } \\ & =bq-\frac{7}{13}q-1b+\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(10+b)(\frac{7}{13}+p)& =(\color{red}{b}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{13}b+10p+10.\frac{7}{13}& \text{Uitwerken } \\ & =bp+\frac{7}{13}b+10p+\frac{70}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-9}{6})(x+\frac{7}{13})& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{13}p+\frac{3}{2}x+\frac{3}{2}.\frac{7}{13}& \text{Uitwerken } \\ & =px+\frac{7}{13}p+\frac{3}{2}x+\frac{21}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{-4}{3})(a-\frac{-14}{18})& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{9}a-\frac{4}{3}a-\frac{4}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =a^2+(\frac{7}{9}+(\frac{-4}{3}))a-(\frac{-28}{27}) & \text{Neem samen} \\ &=a^2-\frac{5}{9}a-(\frac{-28}{27}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(2+x)(a-\frac{10}{18})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{9}x+2a-2.\frac{5}{9}& \text{Uitwerken } \\ & =ax-\frac{5}{9}x+2a-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-19}{15}-q)(\frac{20}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{-19}{15}}).(\color{green}{p}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{10}{3}q-\frac{19}{15}p-\frac{19}{15}.\frac{10}{3}& \text{Uitwerken } \\ & =-pq-\frac{10}{3}q-\frac{19}{15}p-\frac{190}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{10}{3}q-\frac{19}{15}p-\frac{38}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{-10}{5})(x+\frac{9}{5})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{5}q-2x-2.\frac{9}{5}& \text{Uitwerken } \\ & =qx+\frac{9}{5}q-2x-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{15}{14}-p)(\frac{17}{3}-x)& =(\color{red}{-p}+\color{orange}{\frac{15}{14}}).(\color{green}{-x}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{15}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{3}p-\frac{15}{14}x+\frac{15}{14}.\frac{17}{3}& \text{Uitwerken } \\ & =px-\frac{17}{3}p-\frac{15}{14}x+\frac{255}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{3}p-\frac{15}{14}x+\frac{85}{14} & \text{Vereenvoudig} \\\end{align}\)