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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{9}-p)(x-\frac{-1}{2})& =(\color{red}{-p}+\color{orange}{\frac{16}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{16}{9})} . \color{green}{(x)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}p+\frac{16}{9}x+\frac{16}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}p+\frac{16}{9}x+\frac{16}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{2}p+\frac{16}{9}x+\frac{8}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{11}{5}-p)(\frac{-8}{20}+a)& =(\color{red}{-p}+\color{orange}{\frac{11}{5}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{5}p+\frac{11}{5}a-\frac{11}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-ap+\frac{2}{5}p+\frac{11}{5}a-\frac{22}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-1}{15})(\frac{-8}{3}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{15}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{3}x+\frac{1}{15}b-\frac{1}{15}.\frac{8}{3}& \text{Uitwerken } \\ & =bx-\frac{8}{3}x+\frac{1}{15}b-\frac{8}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{9}{11})(\frac{14}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{-9}{11}}).(\color{green}{-a}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(7)} + \color{orange}{(\frac{-9}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -ax+7x+\frac{9}{11}a-\frac{9}{11}.7& \text{Uitwerken } \\ & =-ax+7x+\frac{9}{11}a-\frac{63}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{8}{7})(\frac{-2}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{8}b+\frac{8}{7}a-\frac{8}{7}.\frac{1}{8}& \text{Uitwerken } \\ & =ab-\frac{1}{8}b+\frac{8}{7}a-\frac{8}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{8}b+\frac{8}{7}a-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p+\frac{-2}{7})(\frac{-14}{3}+x)& =(\color{red}{p}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{3}p-\frac{2}{7}x+\frac{2}{7}.\frac{14}{3}& \text{Uitwerken } \\ & =px-\frac{14}{3}p-\frac{2}{7}x+\frac{28}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{14}{3}p-\frac{2}{7}x+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{19}{5}+x)(\frac{6}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{19}{5}}).(\color{green}{b}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{19}{5})} . \color{green}{(b)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{6}{19}x+\frac{19}{5}b+\frac{19}{5}.\frac{6}{19}& \text{Uitwerken } \\ & =bx+\frac{6}{19}x+\frac{19}{5}b+\frac{114}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{6}{19}x+\frac{19}{5}b+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{-6}{5})(q+\frac{2}{4})& =(\color{red}{q}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q+\frac{6}{5}q+\frac{6}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+\frac{6}{5})q+\frac{6}{10} & \text{Neem samen} \\ &=q^2+\frac{17}{10}q+\frac{6}{10} & \text{Maak de som} \\ &=q^2+\frac{17}{10}q+\frac{3}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{-14}{20}-q)(\frac{13}{19}-p)& =(\color{red}{-q}+\color{orange}{\frac{-7}{10}}).(\color{green}{-p}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{19}q+\frac{7}{10}p-\frac{7}{10}.\frac{13}{19}& \text{Uitwerken } \\ & =pq-\frac{13}{19}q+\frac{7}{10}p-\frac{91}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-8}{12}-p)(a-\frac{-11}{12})& =(\color{red}{-p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{12}p-\frac{2}{3}a-\frac{2}{3}.\frac{11}{12}& \text{Uitwerken } \\ & =-ap-\frac{11}{12}p-\frac{2}{3}a-\frac{22}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{11}{12}p-\frac{2}{3}a-\frac{11}{18} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{1}{7}+q)(q-\frac{-9}{15})& =(\color{red}{q}+\color{orange}{\frac{1}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{5}q+\frac{1}{7}q+\frac{1}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =q^2+(\frac{3}{5}+\frac{1}{7})q+\frac{3}{35} & \text{Neem samen} \\ &=q^2+\frac{26}{35}q+\frac{3}{35} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{12}{20}+q)(\frac{7}{10}-b)& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{-b}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{10}q-\frac{3}{5}b+\frac{3}{5}.\frac{7}{10}& \text{Uitwerken } \\ & =-bq+\frac{7}{10}q-\frac{3}{5}b+\frac{21}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)