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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-16}{9})(\frac{-15}{17}-q)& =(\color{red}{a}+\color{orange}{\frac{16}{9}}).(\color{green}{-q}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{16}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{17}a-\frac{16}{9}q-\frac{16}{9}.\frac{15}{17}& \text{Uitwerken } \\ & =-aq-\frac{15}{17}a-\frac{16}{9}q-\frac{240}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{15}{17}a-\frac{16}{9}q-\frac{80}{51} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{4}{12})(\frac{1}{12}-x)& =(\color{red}{x}+\color{orange}{\frac{-1}{3}}).(\color{green}{-x}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{12}x+\frac{1}{3}x-\frac{1}{3}.\frac{1}{12}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{12}+\frac{1}{3})x-\frac{1}{36} & \text{Neem samen} \\ &=-x^2+\frac{5}{12}x-\frac{1}{36} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{17}{5}-b)(\frac{8}{11}+q)& =(\color{red}{-b}+\color{orange}{\frac{17}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{17}{5})} . \color{green}{(q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{11}b+\frac{17}{5}q+\frac{17}{5}.\frac{8}{11}& \text{Uitwerken } \\ & =-bq-\frac{8}{11}b+\frac{17}{5}q+\frac{136}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{6}-p)(p-\frac{-10}{5})& =(\color{red}{-p}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pp-2p-\frac{5}{3}p-\frac{5}{3}.2& \text{Uitwerken } \\ & =-p^2+((-2)+(\frac{-5}{3}))p-\frac{10}{3} & \text{Neem samen} \\ &=-p^2-\frac{11}{3}p-\frac{10}{3} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(p+\frac{-13}{2})((-18)-x)& =(\color{red}{p}+\color{orange}{\frac{-13}{2}}).(\color{green}{-x}+\color{blue}{(-18)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-18)} + \color{orange}{(\frac{-13}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -px-18p+\frac{13}{2}x+\frac{13}{2}.18& \text{Uitwerken } \\ & =-px-18p+\frac{13}{2}x+\frac{234}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-18p+\frac{13}{2}x+117 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{19}{17}+a)(\frac{19}{15}-b)& =(\color{red}{a}+\color{orange}{\frac{19}{17}}).(\color{green}{-b}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{19}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{15}a-\frac{19}{17}b+\frac{19}{17}.\frac{19}{15}& \text{Uitwerken } \\ & =-ab+\frac{19}{15}a-\frac{19}{17}b+\frac{361}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{8}{13})(b-\frac{8}{3})& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{8}{13})} . \color{green}{(b)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{3}a+\frac{8}{13}b-\frac{8}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =ab-\frac{8}{3}a+\frac{8}{13}b-\frac{64}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(2-b)(q-\frac{3}{3})& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1b+2q-2.1& \text{Uitwerken } \\ & =-bq+1b+2q-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{-11}{20})(a-\frac{19}{15})& =(\color{red}{q}+\color{orange}{\frac{-11}{20}}).(\color{green}{a}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{15}q-\frac{11}{20}a+\frac{11}{20}.\frac{19}{15}& \text{Uitwerken } \\ & =aq-\frac{19}{15}q-\frac{11}{20}a+\frac{209}{300} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-20}{10}+p)(\frac{-8}{13}-b)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{8}{13}p+2b+2.\frac{8}{13}& \text{Uitwerken } \\ & =-bp-\frac{8}{13}p+2b+\frac{16}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{16}{16})(q-\frac{-10}{14})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{7}q-1q-1.\frac{5}{7}& \text{Uitwerken } \\ & =q^2+(\frac{5}{7}+(-1))q-(\frac{-5}{7}) & \text{Neem samen} \\ &=q^2-\frac{2}{7}q-(\frac{-5}{7}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q-\frac{17}{15})(x+\frac{16}{10})& =(\color{red}{q}+\color{orange}{\frac{-17}{15}}).(\color{green}{x}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{8}{5}q-\frac{17}{15}x-\frac{17}{15}.\frac{8}{5}& \text{Uitwerken } \\ & =qx+\frac{8}{5}q-\frac{17}{15}x-\frac{136}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)