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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{2}{4}+p)(a+\frac{-3}{11})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{11}p+\frac{1}{2}a-\frac{1}{2}.\frac{3}{11}& \text{Uitwerken } \\ & =ap-\frac{3}{11}p+\frac{1}{2}a-\frac{3}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{1}{17})(p-\frac{6}{11})& =(\color{red}{q}+\color{orange}{\frac{-1}{17}}).(\color{green}{p}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{11}q-\frac{1}{17}p+\frac{1}{17}.\frac{6}{11}& \text{Uitwerken } \\ & =pq-\frac{6}{11}q-\frac{1}{17}p+\frac{6}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{11}+p)(\frac{7}{4}-p)& =(\color{red}{p}+\color{orange}{\frac{-10}{11}}).(\color{green}{-p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{7}{4}p+\frac{10}{11}p-\frac{10}{11}.\frac{7}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{7}{4}+\frac{10}{11})p-\frac{70}{44} & \text{Neem samen} \\ &=-p^2+\frac{117}{44}p-\frac{70}{44} & \text{Maak de som} \\ &=-p^2+\frac{117}{44}p-\frac{35}{22} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(a+18)(\frac{9}{7}+x)& =(\color{red}{a}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{7}a+18x+18.\frac{9}{7}& \text{Uitwerken } \\ & =ax+\frac{9}{7}a+18x+\frac{162}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{15}+q)(\frac{-2}{10}-b)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{-b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{5}q+\frac{2}{5}b+\frac{2}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-bq-\frac{1}{5}q+\frac{2}{5}b+\frac{2}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{8}-b)(b+\frac{14}{16})& =(\color{red}{-b}+\color{orange}{\frac{-7}{8}}).(\color{green}{b}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{8}b-\frac{7}{8}b-\frac{7}{8}.\frac{7}{8}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{8})+(\frac{-7}{8}))b-\frac{49}{64} & \text{Neem samen} \\ &=-b^2-\frac{14}{8}b-\frac{49}{64} & \text{Maak de som} \\ &=-b^2-\frac{7}{4}b-\frac{49}{64} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(p-\frac{16}{19})(p+\frac{12}{15})& =(\color{red}{p}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{5}p-\frac{16}{19}p-\frac{16}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =p^2+(\frac{4}{5}+(\frac{-16}{19}))p-(\frac{-64}{95}) & \text{Neem samen} \\ &=p^2-\frac{4}{95}p-(\frac{-64}{95}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(q+\frac{-15}{4})(q+\frac{13}{11})& =(\color{red}{q}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{13}{11}q-\frac{15}{4}q-\frac{15}{4}.\frac{13}{11}& \text{Uitwerken } \\ & =q^2+(\frac{13}{11}+(\frac{-15}{4}))q-(\frac{-195}{44}) & \text{Neem samen} \\ &=q^2-\frac{113}{44}q-(\frac{-195}{44}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{9}{11}-q)(\frac{11}{8}-x)& =(\color{red}{-q}+\color{orange}{\frac{9}{11}}).(\color{green}{-x}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{9}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{8}q-\frac{9}{11}x+\frac{9}{11}.\frac{11}{8}& \text{Uitwerken } \\ & =qx-\frac{11}{8}q-\frac{9}{11}x+\frac{99}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{11}{8}q-\frac{9}{11}x+\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-9}{4})(\frac{-15}{6}-b)& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{-b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{2}q+\frac{9}{4}b+\frac{9}{4}.\frac{5}{2}& \text{Uitwerken } \\ & =-bq-\frac{5}{2}q+\frac{9}{4}b+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-6}{13})(\frac{7}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{6}{13}}).(\color{green}{p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{6}{13})} . \color{green}{(p)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{2}a+\frac{6}{13}p+\frac{6}{13}.\frac{7}{2}& \text{Uitwerken } \\ & =ap+\frac{7}{2}a+\frac{6}{13}p+\frac{42}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{7}{2}a+\frac{6}{13}p+\frac{21}{13} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{18}{2}-b)(q+\frac{19}{13})& =(\color{red}{-b}+\color{orange}{9}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(9)} . \color{green}{(q)} + \color{orange}{(9)} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{13}b+9q+9.\frac{19}{13}& \text{Uitwerken } \\ & =-bq-\frac{19}{13}b+9q+\frac{171}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)