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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{10}-q)(\frac{-12}{18}+q)& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{2}{3}q+\frac{3}{2}q-\frac{3}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-q^2+(\frac{2}{3}+\frac{3}{2})q-\frac{6}{6} & \text{Neem samen} \\ &=-q^2+\frac{13}{6}q-\frac{6}{6} & \text{Maak de som} \\ &=-q^2+\frac{13}{6}q-1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(b-\frac{-12}{12})(\frac{14}{11}-x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{14}{11}b-1x+1.\frac{14}{11}& \text{Uitwerken } \\ & =-bx+\frac{14}{11}b-1x+\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-19}{2})(q-\frac{-2}{16})& =(\color{red}{b}+\color{orange}{\frac{-19}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{8}b-\frac{19}{2}q-\frac{19}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =bq+\frac{1}{8}b-\frac{19}{2}q-\frac{19}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{20}{18})(\frac{-13}{7}+a)& =(\color{red}{x}+\color{orange}{\frac{10}{9}}).(\color{green}{a}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{7}x+\frac{10}{9}a-\frac{10}{9}.\frac{13}{7}& \text{Uitwerken } \\ & =ax-\frac{13}{7}x+\frac{10}{9}a-\frac{130}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-6}{10})(x-\frac{-5}{13})& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{x}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{13}p-\frac{3}{5}x-\frac{3}{5}.\frac{5}{13}& \text{Uitwerken } \\ & =px+\frac{5}{13}p-\frac{3}{5}x-\frac{15}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{13}p-\frac{3}{5}x-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{14}{14})(b+\frac{17}{7})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{7}x+1b+1.\frac{17}{7}& \text{Uitwerken } \\ & =bx+\frac{17}{7}x+1b+\frac{17}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{13}{10})(b-\frac{-19}{20})& =(\color{red}{p}+\color{orange}{\frac{13}{10}}).(\color{green}{b}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{13}{10})} . \color{green}{(b)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{20}p+\frac{13}{10}b+\frac{13}{10}.\frac{19}{20}& \text{Uitwerken } \\ & =bp+\frac{19}{20}p+\frac{13}{10}b+\frac{247}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{-12}{16})(a+\frac{-17}{12})& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{12}q-\frac{3}{4}a+\frac{3}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =aq-\frac{17}{12}q-\frac{3}{4}a+\frac{51}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{17}{12}q-\frac{3}{4}a+\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p+\frac{-4}{19})(x-\frac{-5}{17})& =(\color{red}{p}+\color{orange}{\frac{-4}{19}}).(\color{green}{x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{17}p-\frac{4}{19}x-\frac{4}{19}.\frac{5}{17}& \text{Uitwerken } \\ & =px+\frac{5}{17}p-\frac{4}{19}x-\frac{20}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{-12}{8})(\frac{-9}{4}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{4}q-\frac{3}{2}a+\frac{3}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =aq-\frac{9}{4}q-\frac{3}{2}a+\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-11}{9}+a)(q-\frac{-3}{17})& =(\color{red}{a}+\color{orange}{\frac{-11}{9}}).(\color{green}{q}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{17}a-\frac{11}{9}q-\frac{11}{9}.\frac{3}{17}& \text{Uitwerken } \\ & =aq+\frac{3}{17}a-\frac{11}{9}q-\frac{33}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{17}a-\frac{11}{9}q-\frac{11}{51} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x+\frac{-6}{3})(q+\frac{-1}{7})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{7}x-2q+2.\frac{1}{7}& \text{Uitwerken } \\ & =qx-\frac{1}{7}x-2q+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)