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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-5}{10})(q-\frac{19}{6})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{6}b-\frac{1}{2}q+\frac{1}{2}.\frac{19}{6}& \text{Uitwerken } \\ & =bq-\frac{19}{6}b-\frac{1}{2}q+\frac{19}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{11}{12}+b)(\frac{-4}{12}+b)& =(\color{red}{b}+\color{orange}{\frac{11}{12}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{11}{12})} . \color{green}{(b)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{3}b+\frac{11}{12}b-\frac{11}{12}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{3})+\frac{11}{12})b-(\frac{-11}{36}) & \text{Neem samen} \\ &=b^2+\frac{7}{12}b-(\frac{-11}{36}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(p+\frac{-20}{19})(q-\frac{-15}{16})& =(\color{red}{p}+\color{orange}{\frac{-20}{19}}).(\color{green}{q}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{16}p-\frac{20}{19}q-\frac{20}{19}.\frac{15}{16}& \text{Uitwerken } \\ & =pq+\frac{15}{16}p-\frac{20}{19}q-\frac{300}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{15}{16}p-\frac{20}{19}q-\frac{75}{76} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-11}{19}-p)(p+\frac{18}{3})& =(\color{red}{-p}+\color{orange}{\frac{-11}{19}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(6)} + \color{orange}{(\frac{-11}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -pp-6p-\frac{11}{19}p-\frac{11}{19}.6& \text{Uitwerken } \\ & =-p^2+((-6)+(\frac{-11}{19}))p-\frac{66}{19} & \text{Neem samen} \\ &=-p^2-\frac{125}{19}p-\frac{66}{19} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{4}{15}+p)(a-\frac{16}{10})& =(\color{red}{p}+\color{orange}{\frac{4}{15}}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{4}{15})} . \color{green}{(a)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{5}p+\frac{4}{15}a-\frac{4}{15}.\frac{8}{5}& \text{Uitwerken } \\ & =ap-\frac{8}{5}p+\frac{4}{15}a-\frac{32}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-14}{14})(q-\frac{-1}{15})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{15}a-1q-1.\frac{1}{15}& \text{Uitwerken } \\ & =aq+\frac{1}{15}a-1q-\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-3}{19})(\frac{-11}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{3}{19}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{3}{19})} . \color{green}{(q)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{18}a+\frac{3}{19}q-\frac{3}{19}.\frac{11}{18}& \text{Uitwerken } \\ & =aq-\frac{11}{18}a+\frac{3}{19}q-\frac{33}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{11}{18}a+\frac{3}{19}q-\frac{11}{114} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b+\frac{-5}{9})(a+(-16))& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-16)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = ab-16b-\frac{5}{9}a+\frac{5}{9}.16& \text{Uitwerken } \\ & =ab-16b-\frac{5}{9}a+\frac{80}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-7}{7}+q)(b-\frac{5}{14})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{14}q-1b+1.\frac{5}{14}& \text{Uitwerken } \\ & =bq-\frac{5}{14}q-1b+\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{12}{17})(\frac{-1}{17}-x)& =(\color{red}{q}+\color{orange}{\frac{-12}{17}}).(\color{green}{-x}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{17}q+\frac{12}{17}x+\frac{12}{17}.\frac{1}{17}& \text{Uitwerken } \\ & =-qx-\frac{1}{17}q+\frac{12}{17}x+\frac{12}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{20}{18}-a)(p+18)& =(\color{red}{-a}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{18})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(18)} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -ap-18a+\frac{10}{9}p+\frac{10}{9}.18& \text{Uitwerken } \\ & =-ap-18a+\frac{10}{9}p+\frac{180}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-18a+\frac{10}{9}p+20 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x+\frac{8}{4})(q+\frac{-20}{18})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{10}{9}x+2q-2.\frac{10}{9}& \text{Uitwerken } \\ & =qx-\frac{10}{9}x+2q-\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)