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

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1. \((\frac{-14}{20}+a)(a-\frac{1}{12})\)
2. \((\frac{-15}{17}+q)(\frac{-1}{9}+a)\)
3. \((\frac{-2}{4}-x)(b+\frac{18}{4})\)
4. \((\frac{12}{20}-x)(\frac{7}{16}-b)\)
5. \((p+\frac{-7}{20})(q-\frac{19}{2})\)
6. \((x+\frac{9}{18})(\frac{-15}{17}-x)\)
7. \((\frac{-14}{8}-q)(a+\frac{-9}{13})\)
8. \((\frac{-18}{13}+q)(\frac{16}{12}-a)\)
9. \((\frac{-14}{10}-p)(\frac{7}{3}-x)\)
10. \((\frac{12}{16}+q)(\frac{-16}{5}-a)\)
11. \((\frac{16}{19}-q)(a+\frac{-5}{18})\)
12. \((\frac{4}{19}+p)(b-\frac{-19}{17})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{20}+a)(a-\frac{1}{12})& =(\color{red}{a}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{12}a-\frac{7}{10}a+\frac{7}{10}.\frac{1}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{12})+(\frac{-7}{10}))a+\frac{7}{120} & \text{Neem samen} \\ &=a^2-\frac{47}{60}a+\frac{7}{120} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-15}{17}+q)(\frac{-1}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{-15}{17}}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{9}q-\frac{15}{17}a+\frac{15}{17}.\frac{1}{9}& \text{Uitwerken } \\ & =aq-\frac{1}{9}q-\frac{15}{17}a+\frac{15}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{9}q-\frac{15}{17}a+\frac{5}{51} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{4}-x)(b+\frac{18}{4})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{2}x-\frac{1}{2}b-\frac{1}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =-bx-\frac{9}{2}x-\frac{1}{2}b-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{12}{20}-x)(\frac{7}{16}-b)& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{-b}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{16}x-\frac{3}{5}b+\frac{3}{5}.\frac{7}{16}& \text{Uitwerken } \\ & =bx-\frac{7}{16}x-\frac{3}{5}b+\frac{21}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-7}{20})(q-\frac{19}{2})& =(\color{red}{p}+\color{orange}{\frac{-7}{20}}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{2}p-\frac{7}{20}q+\frac{7}{20}.\frac{19}{2}& \text{Uitwerken } \\ & =pq-\frac{19}{2}p-\frac{7}{20}q+\frac{133}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{9}{18})(\frac{-15}{17}-x)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{15}{17}x-\frac{1}{2}x-\frac{1}{2}.\frac{15}{17}& \text{Uitwerken } \\ & =-x^2+((\frac{-15}{17})+(\frac{-1}{2}))x-\frac{15}{34} & \text{Neem samen} \\ &=-x^2-\frac{47}{34}x-\frac{15}{34} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{8}-q)(a+\frac{-9}{13})& =(\color{red}{-q}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{13}q-\frac{7}{4}a+\frac{7}{4}.\frac{9}{13}& \text{Uitwerken } \\ & =-aq+\frac{9}{13}q-\frac{7}{4}a+\frac{63}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{13}+q)(\frac{16}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{-18}{13}}).(\color{green}{-a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{4}{3}q+\frac{18}{13}a-\frac{18}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =-aq+\frac{4}{3}q+\frac{18}{13}a-\frac{72}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{4}{3}q+\frac{18}{13}a-\frac{24}{13} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-14}{10}-p)(\frac{7}{3}-x)& =(\color{red}{-p}+\color{orange}{\frac{-7}{5}}).(\color{green}{-x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{3}p+\frac{7}{5}x-\frac{7}{5}.\frac{7}{3}& \text{Uitwerken } \\ & =px-\frac{7}{3}p+\frac{7}{5}x-\frac{49}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{12}{16}+q)(\frac{-16}{5}-a)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{16}{5}q-\frac{3}{4}a-\frac{3}{4}.\frac{16}{5}& \text{Uitwerken } \\ & =-aq-\frac{16}{5}q-\frac{3}{4}a-\frac{48}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{16}{5}q-\frac{3}{4}a-\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{16}{19}-q)(a+\frac{-5}{18})& =(\color{red}{-q}+\color{orange}{\frac{16}{19}}).(\color{green}{a}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{16}{19})} . \color{green}{(a)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{18}q+\frac{16}{19}a-\frac{16}{19}.\frac{5}{18}& \text{Uitwerken } \\ & =-aq+\frac{5}{18}q+\frac{16}{19}a-\frac{80}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{18}q+\frac{16}{19}a-\frac{40}{171} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{4}{19}+p)(b-\frac{-19}{17})& =(\color{red}{p}+\color{orange}{\frac{4}{19}}).(\color{green}{b}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{4}{19})} . \color{green}{(b)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{17}p+\frac{4}{19}b+\frac{4}{19}.\frac{19}{17}& \text{Uitwerken } \\ & =bp+\frac{19}{17}p+\frac{4}{19}b+\frac{76}{323} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{17}p+\frac{4}{19}b+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)