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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{-10}{5})(x+\frac{-16}{10})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{5}x+2x-2.\frac{8}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{5})+2)x-(\frac{-16}{5}) & \text{Neem samen} \\ &=x^2+\frac{2}{5}x-(\frac{-16}{5}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b+\frac{-14}{14})(a-\frac{9}{6})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{2}b-1a+1.\frac{3}{2}& \text{Uitwerken } \\ & =ab-\frac{3}{2}b-1a+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a+\frac{16}{19})(q+\frac{-1}{19})& =(\color{red}{a}+\color{orange}{\frac{16}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{16}{19})} . \color{green}{(q)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{19}a+\frac{16}{19}q-\frac{16}{19}.\frac{1}{19}& \text{Uitwerken } \\ & =aq-\frac{1}{19}a+\frac{16}{19}q-\frac{16}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{19}{15})(q+\frac{20}{19})& =(\color{red}{x}+\color{orange}{\frac{19}{15}}).(\color{green}{q}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{19}{15})} . \color{green}{(q)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{20}{19}x+\frac{19}{15}q+\frac{19}{15}.\frac{20}{19}& \text{Uitwerken } \\ & =qx+\frac{20}{19}x+\frac{19}{15}q+\frac{380}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{20}{19}x+\frac{19}{15}q+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{-8}{7})(x-\frac{-20}{8})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{2}p-\frac{8}{7}x-\frac{8}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =px+\frac{5}{2}p-\frac{8}{7}x-\frac{40}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{2}p-\frac{8}{7}x-\frac{20}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-11}{16}-p)(q+\frac{6}{18})& =(\color{red}{-p}+\color{orange}{\frac{-11}{16}}).(\color{green}{q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}p-\frac{11}{16}q-\frac{11}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}p-\frac{11}{16}q-\frac{11}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-12}{11}+p)((-3)+q)& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-12}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3p-\frac{12}{11}q+\frac{12}{11}.3& \text{Uitwerken } \\ & =pq-3p-\frac{12}{11}q+\frac{36}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{14}{20}-q)(\frac{-18}{13}-q)& =(\color{red}{-q}+\color{orange}{\frac{7}{10}}).(\color{green}{-q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{7}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{18}{13}q-\frac{7}{10}q-\frac{7}{10}.\frac{18}{13}& \text{Uitwerken } \\ & =q^2+(\frac{18}{13}+(\frac{-7}{10}))q-(\frac{-126}{130}) & \text{Neem samen} \\ &=q^2+\frac{89}{130}q-(\frac{-126}{130}) & \text{Maak de som} \\ &=q^2+\frac{89}{130}q+\frac{63}{65} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(q+\frac{8}{16})(a+\frac{14}{17})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{17}q+\frac{1}{2}a+\frac{1}{2}.\frac{14}{17}& \text{Uitwerken } \\ & =aq+\frac{14}{17}q+\frac{1}{2}a+\frac{14}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{14}{17}q+\frac{1}{2}a+\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-20}{13}-b)(a+\frac{-10}{2})& =(\color{red}{-b}+\color{orange}{\frac{-20}{13}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(-5)} + \color{orange}{(\frac{-20}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ab+5b-\frac{20}{13}a+\frac{20}{13}.5& \text{Uitwerken } \\ & =-ab+5b-\frac{20}{13}a+\frac{100}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-19}{20}+q)(x+\frac{-3}{11})& =(\color{red}{q}+\color{orange}{\frac{-19}{20}}).(\color{green}{x}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{11}q-\frac{19}{20}x+\frac{19}{20}.\frac{3}{11}& \text{Uitwerken } \\ & =qx-\frac{3}{11}q-\frac{19}{20}x+\frac{57}{220} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-3}{5})(b-\frac{-15}{10})& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{2}q+\frac{3}{5}b+\frac{3}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =bq+\frac{3}{2}q+\frac{3}{5}b+\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)