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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-3)(p+\frac{-19}{16})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{16}a-3p+3.\frac{19}{16}& \text{Uitwerken } \\ & =ap-\frac{19}{16}a-3p+\frac{57}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{10}{11})(\frac{-11}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{-10}{11}}).(\color{green}{p}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{7}q-\frac{10}{11}p+\frac{10}{11}.\frac{11}{7}& \text{Uitwerken } \\ & =pq-\frac{11}{7}q-\frac{10}{11}p+\frac{110}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{7}q-\frac{10}{11}p+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{19}+a)(x+\frac{-3}{6})& =(\color{red}{a}+\color{orange}{\frac{-13}{19}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a-\frac{13}{19}x+\frac{13}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a-\frac{13}{19}x+\frac{13}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}((-13)-p)(\frac{18}{10}+q)& =(\color{red}{-p}+\color{orange}{(-13)}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-13)} . \color{green}{(q)} + \color{orange}{(-13)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{5}p-13q-13.\frac{9}{5}& \text{Uitwerken } \\ & =-pq-\frac{9}{5}p-13q-\frac{117}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-9}{7})(\frac{4}{12}-p)& =(\color{red}{a}+\color{orange}{\frac{9}{7}}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{9}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}a-\frac{9}{7}p+\frac{9}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}a-\frac{9}{7}p+\frac{9}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{3}a-\frac{9}{7}p+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{7}-a)(q-\frac{9}{19})& =(\color{red}{-a}+\color{orange}{\frac{-19}{7}}).(\color{green}{q}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{19}a-\frac{19}{7}q+\frac{19}{7}.\frac{9}{19}& \text{Uitwerken } \\ & =-aq+\frac{9}{19}a-\frac{19}{7}q+\frac{171}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{19}a-\frac{19}{7}q+\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{17}-b)(\frac{16}{17}+b)& =(\color{red}{-b}+\color{orange}{\frac{-13}{17}}).(\color{green}{b}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{16}{17}b-\frac{13}{17}b-\frac{13}{17}.\frac{16}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-16}{17})+(\frac{-13}{17}))b-\frac{208}{289} & \text{Neem samen} \\ &=-b^2-\frac{29}{17}b-\frac{208}{289} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{17}+p)(\frac{6}{15}+p)& =(\color{red}{p}+\color{orange}{\frac{-18}{17}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{5}p-\frac{18}{17}p-\frac{18}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =p^2+(\frac{2}{5}+(\frac{-18}{17}))p-(\frac{-36}{85}) & \text{Neem samen} \\ &=p^2-\frac{56}{85}p-(\frac{-36}{85}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-1}{19}-b)(\frac{-20}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{-1}{19}}).(\color{green}{-q}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{20}{17}b+\frac{1}{19}q+\frac{1}{19}.\frac{20}{17}& \text{Uitwerken } \\ & =bq+\frac{20}{17}b+\frac{1}{19}q+\frac{20}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{17}{16})(\frac{17}{18}-b)& =(\color{red}{q}+\color{orange}{\frac{-17}{16}}).(\color{green}{-b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{17}{18}q+\frac{17}{16}b-\frac{17}{16}.\frac{17}{18}& \text{Uitwerken } \\ & =-bq+\frac{17}{18}q+\frac{17}{16}b-\frac{289}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{12}+p)(\frac{-11}{7}+q)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{7}p-\frac{3}{4}q+\frac{3}{4}.\frac{11}{7}& \text{Uitwerken } \\ & =pq-\frac{11}{7}p-\frac{3}{4}q+\frac{33}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-18}{2})(\frac{-5}{10}+q)& =(\color{red}{x}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}x+9q-9.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}x+9q-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)