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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-2}{3})(\frac{-14}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{15}q+\frac{2}{3}x-\frac{2}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =qx-\frac{14}{15}q+\frac{2}{3}x-\frac{28}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-15}{7})(\frac{-8}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{15}{7}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bp-2b+\frac{15}{7}p-\frac{15}{7}.2& \text{Uitwerken } \\ & =bp-2b+\frac{15}{7}p-\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-14}{18})(\frac{4}{6}+p)& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{3}q+\frac{7}{9}p+\frac{7}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =pq+\frac{2}{3}q+\frac{7}{9}p+\frac{14}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-19}{12}-a)(\frac{19}{2}-p)& =(\color{red}{-a}+\color{orange}{\frac{-19}{12}}).(\color{green}{-p}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{2}a+\frac{19}{12}p-\frac{19}{12}.\frac{19}{2}& \text{Uitwerken } \\ & =ap-\frac{19}{2}a+\frac{19}{12}p-\frac{361}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-8}{15}+b)(\frac{7}{3}+p)& =(\color{red}{b}+\color{orange}{\frac{-8}{15}}).(\color{green}{p}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{3}b-\frac{8}{15}p-\frac{8}{15}.\frac{7}{3}& \text{Uitwerken } \\ & =bp+\frac{7}{3}b-\frac{8}{15}p-\frac{56}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{-13}{18})(\frac{11}{3}-q)& =(\color{red}{x}+\color{orange}{\frac{13}{18}}).(\color{green}{-q}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{13}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{3}x-\frac{13}{18}q+\frac{13}{18}.\frac{11}{3}& \text{Uitwerken } \\ & =-qx+\frac{11}{3}x-\frac{13}{18}q+\frac{143}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{15}-q)(\frac{1}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{-6}{5}}).(\color{green}{-b}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{9}q+\frac{6}{5}b-\frac{6}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =bq-\frac{1}{9}q+\frac{6}{5}b-\frac{6}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{9}q+\frac{6}{5}b-\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{3}+q)(p+\frac{-19}{7})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{7}q-6p+6.\frac{19}{7}& \text{Uitwerken } \\ & =pq-\frac{19}{7}q-6p+\frac{114}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{5}{14})(q-4)& =(\color{red}{a}+\color{orange}{\frac{5}{14}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4a+\frac{5}{14}q-\frac{5}{14}.4& \text{Uitwerken } \\ & =aq-4a+\frac{5}{14}q-\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4a+\frac{5}{14}q-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{15}{14})(\frac{3}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{-15}{14}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{6}q-\frac{15}{14}b-\frac{15}{14}.\frac{1}{6}& \text{Uitwerken } \\ & =bq+\frac{1}{6}q-\frac{15}{14}b-\frac{15}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{6}q-\frac{15}{14}b-\frac{5}{28} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p-\frac{3}{2})(x-\frac{-4}{17})& =(\color{red}{p}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{17}p-\frac{3}{2}x-\frac{3}{2}.\frac{4}{17}& \text{Uitwerken } \\ & =px+\frac{4}{17}p-\frac{3}{2}x-\frac{12}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{4}{17}p-\frac{3}{2}x-\frac{6}{17} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{5}+a)(\frac{13}{8}-a)& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{-a}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(-4)} . \color{green}{(-a)} + \color{orange}{(-4)} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{13}{8}a+4a-4.\frac{13}{8}& \text{Uitwerken } \\ & =-a^2+(\frac{13}{8}+4)a-\frac{52}{8} & \text{Neem samen} \\ &=-a^2+\frac{45}{8}a-\frac{52}{8} & \text{Maak de som} \\ &=-a^2+\frac{45}{8}a-\frac{13}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)