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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{3}-b)(\frac{14}{19}-q)& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{-q}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(6)} . \color{green}{(-q)} + \color{orange}{(6)} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{19}b-6q+6.\frac{14}{19}& \text{Uitwerken } \\ & =bq-\frac{14}{19}b-6q+\frac{84}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{9}{19})(b+\frac{16}{12})& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{3}p-\frac{9}{19}b-\frac{9}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =bp+\frac{4}{3}p-\frac{9}{19}b-\frac{36}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{3}p-\frac{9}{19}b-\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-5}{13}-p)(x-\frac{12}{2})& =(\color{red}{-p}+\color{orange}{\frac{-5}{13}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-6)} + \color{orange}{(\frac{-5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -px+6p-\frac{5}{13}x+\frac{5}{13}.6& \text{Uitwerken } \\ & =-px+6p-\frac{5}{13}x+\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{-20}{5})(q-\frac{-7}{14})& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{2}b-4q-4.\frac{1}{2}& \text{Uitwerken } \\ & =bq+\frac{1}{2}b-4q-\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{2}b-4q-2 & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{10}-p)(a+\frac{-2}{13})& =(\color{red}{-p}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{13}p-\frac{2}{5}a+\frac{2}{5}.\frac{2}{13}& \text{Uitwerken } \\ & =-ap+\frac{2}{13}p-\frac{2}{5}a+\frac{4}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{-4}{2})(\frac{1}{12}+x)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{12}p+2x+2.\frac{1}{12}& \text{Uitwerken } \\ & =px+\frac{1}{12}p+2x+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{12}p+2x+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{6}-x)(x+\frac{-13}{5})& =(\color{red}{-x}+\color{orange}{\frac{-7}{3}}).(\color{green}{x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{5}x-\frac{7}{3}x+\frac{7}{3}.\frac{13}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{5}+(\frac{-7}{3}))x+(\frac{-91}{15}) & \text{Neem samen} \\ &=-x^2+\frac{4}{15}x+(\frac{-91}{15}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x-\frac{8}{19})(a-\frac{2}{16})& =(\color{red}{x}+\color{orange}{\frac{-8}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{8}x-\frac{8}{19}a+\frac{8}{19}.\frac{1}{8}& \text{Uitwerken } \\ & =ax-\frac{1}{8}x-\frac{8}{19}a+\frac{8}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{8}x-\frac{8}{19}a+\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{15}{4})(p-\frac{-17}{16})& =(\color{red}{q}+\color{orange}{\frac{-15}{4}}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{16}q-\frac{15}{4}p-\frac{15}{4}.\frac{17}{16}& \text{Uitwerken } \\ & =pq+\frac{17}{16}q-\frac{15}{4}p-\frac{255}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{10}+a)(\frac{14}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{-p}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{14}{9}a-\frac{4}{5}p+\frac{4}{5}.\frac{14}{9}& \text{Uitwerken } \\ & =-ap+\frac{14}{9}a-\frac{4}{5}p+\frac{56}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{2}{11}+a)(a-\frac{8}{10})& =(\color{red}{a}+\color{orange}{\frac{2}{11}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{2}{11})} . \color{green}{(a)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{5}a+\frac{2}{11}a-\frac{2}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{5})+\frac{2}{11})a-(\frac{-8}{55}) & \text{Neem samen} \\ &=a^2-\frac{34}{55}a-(\frac{-8}{55}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q+\frac{-2}{6})(\frac{-6}{17}+a)& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{17}q-\frac{1}{3}a+\frac{1}{3}.\frac{6}{17}& \text{Uitwerken } \\ & =aq-\frac{6}{17}q-\frac{1}{3}a+\frac{6}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{6}{17}q-\frac{1}{3}a+\frac{2}{17} & \text{Vereenvoudig} \\\end{align}\)