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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{14}-q)(\frac{-6}{13}+q)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{6}{13}q-1q+1.\frac{6}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{6}{13}+(-1))q+(\frac{-6}{13}) & \text{Neem samen} \\ &=-q^2-\frac{7}{13}q+(\frac{-6}{13}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(q-\frac{9}{20})(x+\frac{-5}{8})& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{x}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{8}q-\frac{9}{20}x+\frac{9}{20}.\frac{5}{8}& \text{Uitwerken } \\ & =qx-\frac{5}{8}q-\frac{9}{20}x+\frac{45}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{8}q-\frac{9}{20}x+\frac{9}{32} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}((-20)+p)(x-\frac{4}{2})& =(\color{red}{p}+\color{orange}{(-20)}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(-20)} . \color{green}{(x)} + \color{orange}{(-20)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-20x+20.2& \text{Uitwerken } \\ & =px-2p-20x+40 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{9}+x)(\frac{-14}{3}+a)& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{14}{3}x-\frac{10}{9}a+\frac{10}{9}.\frac{14}{3}& \text{Uitwerken } \\ & =ax-\frac{14}{3}x-\frac{10}{9}a+\frac{140}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{13}+q)(b+\frac{-5}{9})& =(\color{red}{q}+\color{orange}{\frac{-1}{13}}).(\color{green}{b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{9}q-\frac{1}{13}b+\frac{1}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =bq-\frac{5}{9}q-\frac{1}{13}b+\frac{5}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{20}{5})(\frac{-15}{9}+b)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{3}a+4b-4.\frac{5}{3}& \text{Uitwerken } \\ & =ab-\frac{5}{3}a+4b-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{1}{18})(\frac{-9}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{1}{18}}).(\color{green}{a}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{1}{18})} . \color{green}{(a)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{16}x+\frac{1}{18}a-\frac{1}{18}.\frac{9}{16}& \text{Uitwerken } \\ & =ax-\frac{9}{16}x+\frac{1}{18}a-\frac{9}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{16}x+\frac{1}{18}a-\frac{1}{32} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p-\frac{-1}{13})(a+\frac{2}{18})& =(\color{red}{p}+\color{orange}{\frac{1}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{9}p+\frac{1}{13}a+\frac{1}{13}.\frac{1}{9}& \text{Uitwerken } \\ & =ap+\frac{1}{9}p+\frac{1}{13}a+\frac{1}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{12}+b)(\frac{-3}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{14}b+\frac{1}{4}b+\frac{1}{4}.\frac{3}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{14})+\frac{1}{4})b+(\frac{-3}{56}) & \text{Neem samen} \\ &=-b^2+\frac{1}{28}b+(\frac{-3}{56}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-7}{6}+a)(\frac{13}{20}+a)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{13}{20}a-\frac{7}{6}a-\frac{7}{6}.\frac{13}{20}& \text{Uitwerken } \\ & =a^2+(\frac{13}{20}+(\frac{-7}{6}))a-(\frac{-91}{120}) & \text{Neem samen} \\ &=a^2-\frac{31}{60}a-(\frac{-91}{120}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(a-\frac{2}{13})(\frac{-12}{10}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{5}a-\frac{2}{13}x+\frac{2}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =ax-\frac{6}{5}a-\frac{2}{13}x+\frac{12}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{7}{6})(\frac{8}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{-7}{6}}).(\color{green}{-q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{2}{5}p+\frac{7}{6}q-\frac{7}{6}.\frac{2}{5}& \text{Uitwerken } \\ & =-pq+\frac{2}{5}p+\frac{7}{6}q-\frac{14}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{2}{5}p+\frac{7}{6}q-\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)