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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-3}{15})(\frac{-20}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{20}{19}a+\frac{1}{5}a-\frac{1}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-20}{19})+\frac{1}{5})a-(\frac{-20}{95}) & \text{Neem samen} \\ &=a^2-\frac{81}{95}a-(\frac{-20}{95}) & \text{Maak de som} \\ &=a^2-\frac{81}{95}a+\frac{4}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(q+\frac{-19}{9})(p+\frac{-16}{11})& =(\color{red}{q}+\color{orange}{\frac{-19}{9}}).(\color{green}{p}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{11}q-\frac{19}{9}p+\frac{19}{9}.\frac{16}{11}& \text{Uitwerken } \\ & =pq-\frac{16}{11}q-\frac{19}{9}p+\frac{304}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{17}{18}+a)(\frac{-12}{11}-q)& =(\color{red}{a}+\color{orange}{\frac{17}{18}}).(\color{green}{-q}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(\frac{17}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{12}{11}a-\frac{17}{18}q-\frac{17}{18}.\frac{12}{11}& \text{Uitwerken } \\ & =-aq-\frac{12}{11}a-\frac{17}{18}q-\frac{204}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{12}{11}a-\frac{17}{18}q-\frac{34}{33} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{20}{17})(p-12)& =(\color{red}{p}+\color{orange}{\frac{20}{17}}).(\color{green}{p}+\color{blue}{(-12)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-12)} + \color{orange}{(\frac{20}{17})} . \color{green}{(p)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = pp-12p+\frac{20}{17}p-\frac{20}{17}.12& \text{Uitwerken } \\ & =p^2+((-12)+\frac{20}{17})p-(\frac{-240}{17}) & \text{Neem samen} \\ &=p^2-\frac{184}{17}p-(\frac{-240}{17}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{19}{8}+b)(p-\frac{-19}{11})& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{19}{8})} . \color{green}{(p)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{11}b+\frac{19}{8}p+\frac{19}{8}.\frac{19}{11}& \text{Uitwerken } \\ & =bp+\frac{19}{11}b+\frac{19}{8}p+\frac{361}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-9}{8})(\frac{-19}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{-9}{8}}).(\color{green}{-q}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{14}x+\frac{9}{8}q+\frac{9}{8}.\frac{19}{14}& \text{Uitwerken } \\ & =-qx-\frac{19}{14}x+\frac{9}{8}q+\frac{171}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{14}{7})(\frac{3}{16}-p)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-p}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(2)} . \color{green}{(-p)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{16}b-2p+2.\frac{3}{16}& \text{Uitwerken } \\ & =-bp+\frac{3}{16}b-2p+\frac{6}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{3}{16}b-2p+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b-\frac{2}{17})(q+\frac{1}{19})& =(\color{red}{b}+\color{orange}{\frac{-2}{17}}).(\color{green}{q}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{19}b-\frac{2}{17}q-\frac{2}{17}.\frac{1}{19}& \text{Uitwerken } \\ & =bq+\frac{1}{19}b-\frac{2}{17}q-\frac{2}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{1}{11}+b)(\frac{-7}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{-b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{1}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{4}b-\frac{1}{11}b-\frac{1}{11}.\frac{7}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{4})+(\frac{-1}{11}))b-\frac{7}{44} & \text{Neem samen} \\ &=-b^2-\frac{81}{44}b-\frac{7}{44} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{3}{4})(x-\frac{-19}{12})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{12}a+\frac{3}{4}x+\frac{3}{4}.\frac{19}{12}& \text{Uitwerken } \\ & =ax+\frac{19}{12}a+\frac{3}{4}x+\frac{57}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{19}{12}a+\frac{3}{4}x+\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{7}{6})(\frac{-14}{17}+b)& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{b}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{17}q-\frac{7}{6}b+\frac{7}{6}.\frac{14}{17}& \text{Uitwerken } \\ & =bq-\frac{14}{17}q-\frac{7}{6}b+\frac{98}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{14}{17}q-\frac{7}{6}b+\frac{49}{51} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{-4}{11})(x-\frac{-4}{16})& =(\color{red}{q}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-\frac{4}{11}x-\frac{4}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-\frac{4}{11}x-\frac{4}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{4}q-\frac{4}{11}x-\frac{1}{11} & \text{Vereenvoudig} \\\end{align}\)