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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-12}{16}+x)(\frac{-20}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{13}x+\frac{3}{4}q+\frac{3}{4}.\frac{20}{13}& \text{Uitwerken } \\ & =-qx-\frac{20}{13}x+\frac{3}{4}q+\frac{60}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{20}{13}x+\frac{3}{4}q+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-1}{8})(q-\frac{-11}{15})& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{11}{15}p+\frac{1}{8}q+\frac{1}{8}.\frac{11}{15}& \text{Uitwerken } \\ & =pq+\frac{11}{15}p+\frac{1}{8}q+\frac{11}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{20}{20}+b)(\frac{10}{19}-x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{10}{19}b-1x+1.\frac{10}{19}& \text{Uitwerken } \\ & =-bx+\frac{10}{19}b-1x+\frac{10}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{6}{8})(\frac{6}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}q-\frac{3}{4}b-\frac{3}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}q-\frac{3}{4}b-\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{3}q-\frac{3}{4}b-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{11}{13}+q)(p+\frac{3}{4})& =(\color{red}{q}+\color{orange}{\frac{11}{13}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{4}q+\frac{11}{13}p+\frac{11}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =pq+\frac{3}{4}q+\frac{11}{13}p+\frac{33}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{10}-x)(p+\frac{-16}{16})& =(\color{red}{-x}+\color{orange}{\frac{-9}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px+1x-\frac{9}{5}p+\frac{9}{5}.1& \text{Uitwerken } \\ & =-px+1x-\frac{9}{5}p+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{16}{16})(b-\frac{19}{10})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{10}x-1b+1.\frac{19}{10}& \text{Uitwerken } \\ & =bx-\frac{19}{10}x-1b+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-3}{15}+p)(a-\frac{-2}{17})& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{17}p-\frac{1}{5}a-\frac{1}{5}.\frac{2}{17}& \text{Uitwerken } \\ & =ap+\frac{2}{17}p-\frac{1}{5}a-\frac{2}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{4}{4})(\frac{15}{12}+a)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{4}p-1a-1.\frac{5}{4}& \text{Uitwerken } \\ & =ap+\frac{5}{4}p-1a-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-1}{17}+b)(x-\frac{-17}{12})& =(\color{red}{b}+\color{orange}{\frac{-1}{17}}).(\color{green}{x}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{12}b-\frac{1}{17}x-\frac{1}{17}.\frac{17}{12}& \text{Uitwerken } \\ & =bx+\frac{17}{12}b-\frac{1}{17}x-\frac{17}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{17}{12}b-\frac{1}{17}x-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-5}{14}-p)(q+\frac{-15}{6})& =(\color{red}{-p}+\color{orange}{\frac{-5}{14}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{2}p-\frac{5}{14}q+\frac{5}{14}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq+\frac{5}{2}p-\frac{5}{14}q+\frac{25}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{2}{3}+x)(\frac{11}{6}+a)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{6}x+\frac{2}{3}a+\frac{2}{3}.\frac{11}{6}& \text{Uitwerken } \\ & =ax+\frac{11}{6}x+\frac{2}{3}a+\frac{22}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{6}x+\frac{2}{3}a+\frac{11}{9} & \text{Vereenvoudig} \\\end{align}\)