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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-5}{12})(\frac{5}{20}-p)& =(\color{red}{q}+\color{orange}{\frac{5}{12}}).(\color{green}{-p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{4}q-\frac{5}{12}p+\frac{5}{12}.\frac{1}{4}& \text{Uitwerken } \\ & =-pq+\frac{1}{4}q-\frac{5}{12}p+\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-16}{18})(\frac{18}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2p+\frac{8}{9}a+\frac{8}{9}.2& \text{Uitwerken } \\ & =ap+2p+\frac{8}{9}a+\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-8}{3}-b)(\frac{15}{7}-q)& =(\color{red}{-b}+\color{orange}{\frac{-8}{3}}).(\color{green}{-q}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{7}b+\frac{8}{3}q-\frac{8}{3}.\frac{15}{7}& \text{Uitwerken } \\ & =bq-\frac{15}{7}b+\frac{8}{3}q-\frac{120}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{15}{7}b+\frac{8}{3}q-\frac{40}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p-\frac{-8}{18})(\frac{10}{9}-p)& =(\color{red}{p}+\color{orange}{\frac{4}{9}}).(\color{green}{-p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{10}{9}p-\frac{4}{9}p+\frac{4}{9}.\frac{10}{9}& \text{Uitwerken } \\ & =-p^2+(\frac{10}{9}+(\frac{-4}{9}))p+(\frac{-40}{81}) & \text{Neem samen} \\ &=-p^2+\frac{6}{9}p+(\frac{-40}{81}) & \text{Maak de som} \\ &=-p^2+\frac{2}{3}p+(\frac{-40}{81}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{6}{5}+a)(\frac{2}{2}-p)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a-\frac{6}{5}p+\frac{6}{5}.1& \text{Uitwerken } \\ & =-ap+1a-\frac{6}{5}p+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{15}{13})(a+\frac{-13}{14})& =(\color{red}{a}+\color{orange}{\frac{15}{13}}).(\color{green}{a}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{15}{13})} . \color{green}{(a)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{14}a+\frac{15}{13}a-\frac{15}{13}.\frac{13}{14}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{14})+\frac{15}{13})a-(\frac{-195}{182}) & \text{Neem samen} \\ &=a^2+\frac{41}{182}a-(\frac{-195}{182}) & \text{Maak de som} \\ &=a^2+\frac{41}{182}a+\frac{15}{14} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(x+\frac{1}{6})(\frac{15}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{2}x+\frac{1}{6}b+\frac{1}{6}.\frac{15}{2}& \text{Uitwerken } \\ & =bx+\frac{15}{2}x+\frac{1}{6}b+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{2}x+\frac{1}{6}b+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b-\frac{7}{15})(q+\frac{-17}{15})& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{q}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{15}b-\frac{7}{15}q+\frac{7}{15}.\frac{17}{15}& \text{Uitwerken } \\ & =bq-\frac{17}{15}b-\frac{7}{15}q+\frac{119}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-1}{9})(x-\frac{14}{10})& =(\color{red}{x}+\color{orange}{\frac{-1}{9}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{5}x-\frac{1}{9}x+\frac{1}{9}.\frac{7}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{5})+(\frac{-1}{9}))x+\frac{7}{45} & \text{Neem samen} \\ &=x^2-\frac{68}{45}x+\frac{7}{45} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q+\frac{-1}{15})(\frac{7}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{15}}).(\color{green}{-p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{5}q+\frac{1}{15}p-\frac{1}{15}.\frac{7}{5}& \text{Uitwerken } \\ & =-pq+\frac{7}{5}q+\frac{1}{15}p-\frac{7}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q+\frac{-7}{8})(x-\frac{10}{19})& =(\color{red}{q}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{19}q-\frac{7}{8}x+\frac{7}{8}.\frac{10}{19}& \text{Uitwerken } \\ & =qx-\frac{10}{19}q-\frac{7}{8}x+\frac{70}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{10}{19}q-\frac{7}{8}x+\frac{35}{76} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x+\frac{-12}{3})(\frac{6}{7}+q)& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{7}x-4q-4.\frac{6}{7}& \text{Uitwerken } \\ & =qx+\frac{6}{7}x-4q-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)