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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{7}{12})(\frac{10}{9}+b)& =(\color{red}{q}+\color{orange}{\frac{-7}{12}}).(\color{green}{b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{9}q-\frac{7}{12}b-\frac{7}{12}.\frac{10}{9}& \text{Uitwerken } \\ & =bq+\frac{10}{9}q-\frac{7}{12}b-\frac{70}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{10}{9}q-\frac{7}{12}b-\frac{35}{54} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{20}+q)(\frac{-3}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1q+\frac{1}{2}a+\frac{1}{2}.1& \text{Uitwerken } \\ & =-aq-1q+\frac{1}{2}a+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{2}{18}+q)(\frac{-1}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}q-\frac{1}{9}p-\frac{1}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}q-\frac{1}{9}p-\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{16}{5})(\frac{-4}{4}+p)& =(\color{red}{a}+\color{orange}{\frac{16}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{16}{5})} . \color{green}{(p)} + \color{orange}{(\frac{16}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{16}{5}p-\frac{16}{5}.1& \text{Uitwerken } \\ & =ap-1a+\frac{16}{5}p-\frac{16}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-18}{20}+x)(p+\frac{-7}{14})& =(\color{red}{x}+\color{orange}{\frac{-9}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{2}x-\frac{9}{10}p+\frac{9}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =px-\frac{1}{2}x-\frac{9}{10}p+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{-4}{11})(a-\frac{14}{12})& =(\color{red}{q}+\color{orange}{\frac{4}{11}}).(\color{green}{a}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{4}{11})} . \color{green}{(a)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{6}q+\frac{4}{11}a-\frac{4}{11}.\frac{7}{6}& \text{Uitwerken } \\ & =aq-\frac{7}{6}q+\frac{4}{11}a-\frac{28}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{6}q+\frac{4}{11}a-\frac{14}{33} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x+\frac{19}{19})(\frac{-1}{12}-a)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{12}x-1a-1.\frac{1}{12}& \text{Uitwerken } \\ & =-ax-\frac{1}{12}x-1a-\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-9)(b+\frac{-2}{10})& =(\color{red}{a}+\color{orange}{(-9)}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-9)} . \color{green}{(b)} + \color{orange}{(-9)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{5}a-9b+9.\frac{1}{5}& \text{Uitwerken } \\ & =ab-\frac{1}{5}a-9b+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-6}{2}-q)(a-\frac{5}{5})& =(\color{red}{-q}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q-3a+3.1& \text{Uitwerken } \\ & =-aq+1q-3a+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{14}-a)(\frac{-9}{10}+p)& =(\color{red}{-a}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{10}a-\frac{8}{7}p+\frac{8}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =-ap+\frac{9}{10}a-\frac{8}{7}p+\frac{72}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{9}{10}a-\frac{8}{7}p+\frac{36}{35} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-1}{2}+a)(a-\frac{-9}{5})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{5}a-\frac{1}{2}a-\frac{1}{2}.\frac{9}{5}& \text{Uitwerken } \\ & =a^2+(\frac{9}{5}+(\frac{-1}{2}))a-(\frac{-9}{10}) & \text{Neem samen} \\ &=a^2+\frac{13}{10}a-(\frac{-9}{10}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p+\frac{-5}{11})(\frac{-4}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{11}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{3}p-\frac{5}{11}b+\frac{5}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =bp-\frac{2}{3}p-\frac{5}{11}b+\frac{10}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)