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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{16}{5})(q+\frac{16}{16})& =(\color{red}{b}+\color{orange}{\frac{16}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{5})} . \color{green}{(q)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b+\frac{16}{5}q+\frac{16}{5}.1& \text{Uitwerken } \\ & =bq+1b+\frac{16}{5}q+\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{20}{18})(p+\frac{17}{16})& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{16}x+\frac{10}{9}p+\frac{10}{9}.\frac{17}{16}& \text{Uitwerken } \\ & =px+\frac{17}{16}x+\frac{10}{9}p+\frac{170}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{17}{16}x+\frac{10}{9}p+\frac{85}{72} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{1}{12})(a-\frac{11}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{12}}).(\color{green}{a}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{8}q-\frac{1}{12}a+\frac{1}{12}.\frac{11}{8}& \text{Uitwerken } \\ & =aq-\frac{11}{8}q-\frac{1}{12}a+\frac{11}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{-5}{6})(a-\frac{18}{19})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{19}q-\frac{5}{6}a+\frac{5}{6}.\frac{18}{19}& \text{Uitwerken } \\ & =aq-\frac{18}{19}q-\frac{5}{6}a+\frac{90}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{18}{19}q-\frac{5}{6}a+\frac{15}{19} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}((-5)+q)(a-\frac{-18}{16})& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(-5)} . \color{green}{(a)} + \color{orange}{(-5)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{8}q-5a-5.\frac{9}{8}& \text{Uitwerken } \\ & =aq+\frac{9}{8}q-5a-\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{14}{11})(p+\frac{-17}{15})& =(\color{red}{q}+\color{orange}{\frac{14}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{14}{11})} . \color{green}{(p)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{15}q+\frac{14}{11}p-\frac{14}{11}.\frac{17}{15}& \text{Uitwerken } \\ & =pq-\frac{17}{15}q+\frac{14}{11}p-\frac{238}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{4}-b)(\frac{13}{8}-b)& =(\color{red}{-b}+\color{orange}{\frac{7}{4}}).(\color{green}{-b}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{7}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{13}{8}b-\frac{7}{4}b+\frac{7}{4}.\frac{13}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-13}{8})+(\frac{-7}{4}))b+\frac{91}{32} & \text{Neem samen} \\ &=b^2-\frac{27}{8}b+\frac{91}{32} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p+\frac{5}{13})(\frac{15}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{5}{13}}).(\color{green}{p}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{5}{13})} . \color{green}{(p)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{7}p+\frac{5}{13}p+\frac{5}{13}.\frac{15}{7}& \text{Uitwerken } \\ & =p^2+(\frac{15}{7}+\frac{5}{13})p+\frac{75}{91} & \text{Neem samen} \\ &=p^2+\frac{230}{91}p+\frac{75}{91} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{17}-q)(p-\frac{-12}{7})& =(\color{red}{-q}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{12}{7}q-\frac{13}{17}p-\frac{13}{17}.\frac{12}{7}& \text{Uitwerken } \\ & =-pq-\frac{12}{7}q-\frac{13}{17}p-\frac{156}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{1}{20})(q+(-20))& =(\color{red}{b}+\color{orange}{\frac{-1}{20}}).(\color{green}{q}+\color{blue}{(-20)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-20)} + \color{orange}{(\frac{-1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = bq-20b-\frac{1}{20}q+\frac{1}{20}.20& \text{Uitwerken } \\ & =bq-20b-\frac{1}{20}q+\frac{20}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-20b-\frac{1}{20}q+1 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{18}+b)(p-\frac{-20}{3})& =(\color{red}{b}+\color{orange}{\frac{-7}{18}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{3}b-\frac{7}{18}p-\frac{7}{18}.\frac{20}{3}& \text{Uitwerken } \\ & =bp+\frac{20}{3}b-\frac{7}{18}p-\frac{140}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{20}{3}b-\frac{7}{18}p-\frac{70}{27} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}((-5)+p)(x+\frac{-17}{10})& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{10}p-5x+5.\frac{17}{10}& \text{Uitwerken } \\ & =px-\frac{17}{10}p-5x+\frac{85}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{10}p-5x+\frac{17}{2} & \text{Vereenvoudig} \\\end{align}\)