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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-15}{6})(x-\frac{-11}{6})& =(\color{red}{q}+\color{orange}{\frac{5}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{6}q+\frac{5}{2}x+\frac{5}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =qx+\frac{11}{6}q+\frac{5}{2}x+\frac{55}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{12}-x)(a+\frac{-13}{4})& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{4}x-\frac{1}{3}a+\frac{1}{3}.\frac{13}{4}& \text{Uitwerken } \\ & =-ax+\frac{13}{4}x-\frac{1}{3}a+\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{19}{15})(\frac{6}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{-19}{15}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}p-\frac{19}{15}b-\frac{19}{15}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}p-\frac{19}{15}b-\frac{38}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{12}-a)(\frac{2}{4}-q)& =(\color{red}{-a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}a+\frac{3}{4}q-\frac{3}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}a+\frac{3}{4}q-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-19}{16}-q)(x-\frac{-15}{11})& =(\color{red}{-q}+\color{orange}{\frac{-19}{16}}).(\color{green}{x}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{11}q-\frac{19}{16}x-\frac{19}{16}.\frac{15}{11}& \text{Uitwerken } \\ & =-qx-\frac{15}{11}q-\frac{19}{16}x-\frac{285}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{3}{3}+p)(\frac{10}{17}+q)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{10}{17}p+1q+1.\frac{10}{17}& \text{Uitwerken } \\ & =pq+\frac{10}{17}p+1q+\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{-8}{15})(\frac{-20}{11}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{11}b+\frac{8}{15}a-\frac{8}{15}.\frac{20}{11}& \text{Uitwerken } \\ & =ab-\frac{20}{11}b+\frac{8}{15}a-\frac{160}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{11}b+\frac{8}{15}a-\frac{32}{33} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q+\frac{-4}{12})(a+\frac{-11}{7})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{7}q-\frac{1}{3}a+\frac{1}{3}.\frac{11}{7}& \text{Uitwerken } \\ & =aq-\frac{11}{7}q-\frac{1}{3}a+\frac{11}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-1}{8}+b)(b+\frac{-17}{2})& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{2}b-\frac{1}{8}b+\frac{1}{8}.\frac{17}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{2})+(\frac{-1}{8}))b+\frac{17}{16} & \text{Neem samen} \\ &=b^2-\frac{69}{8}b+\frac{17}{16} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-14}{10}+q)(b+\frac{1}{6})& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{6}q-\frac{7}{5}b-\frac{7}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =bq+\frac{1}{6}q-\frac{7}{5}b-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{11}{10})(\frac{17}{14}-b)& =(\color{red}{a}+\color{orange}{\frac{11}{10}}).(\color{green}{-b}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{11}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{14}a-\frac{11}{10}b+\frac{11}{10}.\frac{17}{14}& \text{Uitwerken } \\ & =-ab+\frac{17}{14}a-\frac{11}{10}b+\frac{187}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{8}{13}+x)(a+\frac{2}{8})& =(\color{red}{x}+\color{orange}{\frac{8}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}x+\frac{8}{13}a+\frac{8}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}x+\frac{8}{13}a+\frac{8}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{4}x+\frac{8}{13}a+\frac{2}{13} & \text{Vereenvoudig} \\\end{align}\)