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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{-5}{8})(\frac{9}{3}-a)& =(\color{red}{q}+\color{orange}{\frac{-5}{8}}).(\color{green}{-a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -aq+3q+\frac{5}{8}a-\frac{5}{8}.3& \text{Uitwerken } \\ & =-aq+3q+\frac{5}{8}a-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{9}{4})(a+\frac{2}{12})& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{6}q+\frac{9}{4}a+\frac{9}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =aq+\frac{1}{6}q+\frac{9}{4}a+\frac{9}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{6}q+\frac{9}{4}a+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x+\frac{-1}{14})(\frac{-11}{5}-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{14}}).(\color{green}{-p}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{11}{5}x+\frac{1}{14}p+\frac{1}{14}.\frac{11}{5}& \text{Uitwerken } \\ & =-px-\frac{11}{5}x+\frac{1}{14}p+\frac{11}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{8}{19}-q)(b+\frac{-1}{8})& =(\color{red}{-q}+\color{orange}{\frac{8}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{8}{19})} . \color{green}{(b)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{8}q+\frac{8}{19}b-\frac{8}{19}.\frac{1}{8}& \text{Uitwerken } \\ & =-bq+\frac{1}{8}q+\frac{8}{19}b-\frac{8}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{8}q+\frac{8}{19}b-\frac{1}{19} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a-\frac{-11}{19})(q+\frac{14}{2})& =(\color{red}{a}+\color{orange}{\frac{11}{19}}).(\color{green}{q}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = aq+7a+\frac{11}{19}q+\frac{11}{19}.7& \text{Uitwerken } \\ & =aq+7a+\frac{11}{19}q+\frac{77}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-6}{11}+b)(\frac{-17}{14}+x)& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{x}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{14}b-\frac{6}{11}x+\frac{6}{11}.\frac{17}{14}& \text{Uitwerken } \\ & =bx-\frac{17}{14}b-\frac{6}{11}x+\frac{102}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{17}{14}b-\frac{6}{11}x+\frac{51}{77} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{14}{19}+p)(\frac{10}{19}-q)& =(\color{red}{p}+\color{orange}{\frac{14}{19}}).(\color{green}{-q}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{10}{19}p-\frac{14}{19}q+\frac{14}{19}.\frac{10}{19}& \text{Uitwerken } \\ & =-pq+\frac{10}{19}p-\frac{14}{19}q+\frac{140}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-14}{11})(p+\frac{6}{2})& =(\color{red}{x}+\color{orange}{\frac{-14}{11}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-14}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = px+3x-\frac{14}{11}p-\frac{14}{11}.3& \text{Uitwerken } \\ & =px+3x-\frac{14}{11}p-\frac{42}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-12}{2})(\frac{17}{20}-a)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{-a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(-6)} . \color{green}{(-a)} + \color{orange}{(-6)} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{20}x+6a-6.\frac{17}{20}& \text{Uitwerken } \\ & =-ax+\frac{17}{20}x+6a-\frac{102}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{17}{20}x+6a-\frac{51}{10} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-\frac{15}{6})(x-\frac{-7}{8})& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{8}x-\frac{5}{2}x-\frac{5}{2}.\frac{7}{8}& \text{Uitwerken } \\ & =x^2+(\frac{7}{8}+(\frac{-5}{2}))x-(\frac{-35}{16}) & \text{Neem samen} \\ &=x^2-\frac{13}{8}x-(\frac{-35}{16}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{5}+p)(\frac{3}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{-q}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{13}p+\frac{7}{5}q-\frac{7}{5}.\frac{3}{13}& \text{Uitwerken } \\ & =-pq+\frac{3}{13}p+\frac{7}{5}q-\frac{21}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{19}{8})(\frac{-6}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{19}{8}}).(\color{green}{-q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{13}x-\frac{19}{8}q-\frac{19}{8}.\frac{6}{13}& \text{Uitwerken } \\ & =-qx-\frac{6}{13}x-\frac{19}{8}q-\frac{114}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{13}x-\frac{19}{8}q-\frac{57}{52} & \text{Vereenvoudig} \\\end{align}\)