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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-3}{10}-p)(\frac{1}{4}-q)& =(\color{red}{-p}+\color{orange}{\frac{-3}{10}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}p+\frac{3}{10}q-\frac{3}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}p+\frac{3}{10}q-\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-5}{20})(\frac{-18}{2}-a)& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{-a}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-9)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -ax-9x+\frac{1}{4}a+\frac{1}{4}.9& \text{Uitwerken } \\ & =-ax-9x+\frac{1}{4}a+\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{2}{16}-a)(\frac{15}{5}+a)& =(\color{red}{-a}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -aa-3a+\frac{1}{8}a+\frac{1}{8}.3& \text{Uitwerken } \\ & =-a^2+((-3)+\frac{1}{8})a+(\frac{-3}{8}) & \text{Neem samen} \\ &=-a^2-\frac{23}{8}a+(\frac{-3}{8}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q-\frac{-8}{17})(\frac{-9}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{8}{17}}).(\color{green}{-b}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{8}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{9}{13}q-\frac{8}{17}b-\frac{8}{17}.\frac{9}{13}& \text{Uitwerken } \\ & =-bq-\frac{9}{13}q-\frac{8}{17}b-\frac{72}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-7}{19}-x)(\frac{19}{16}+p)& =(\color{red}{-x}+\color{orange}{\frac{-7}{19}}).(\color{green}{p}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{16}x-\frac{7}{19}p-\frac{7}{19}.\frac{19}{16}& \text{Uitwerken } \\ & =-px-\frac{19}{16}x-\frac{7}{19}p-\frac{133}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{19}{16}x-\frac{7}{19}p-\frac{7}{16} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q-\frac{17}{12})(p-\frac{17}{6})& =(\color{red}{q}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{6}q-\frac{17}{12}p+\frac{17}{12}.\frac{17}{6}& \text{Uitwerken } \\ & =pq-\frac{17}{6}q-\frac{17}{12}p+\frac{289}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{14}{3}-b)(b+\frac{-2}{16})& =(\color{red}{-b}+\color{orange}{\frac{14}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{14}{3})} . \color{green}{(b)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{8}b+\frac{14}{3}b-\frac{14}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{8}+\frac{14}{3})b-\frac{14}{24} & \text{Neem samen} \\ &=-b^2+\frac{115}{24}b-\frac{14}{24} & \text{Maak de som} \\ &=-b^2+\frac{115}{24}b-\frac{7}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{14}+q)(q-\frac{-10}{4})& =(\color{red}{q}+\color{orange}{\frac{-9}{14}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{2}q-\frac{9}{14}q-\frac{9}{14}.\frac{5}{2}& \text{Uitwerken } \\ & =q^2+(\frac{5}{2}+(\frac{-9}{14}))q-(\frac{-45}{28}) & \text{Neem samen} \\ &=q^2+\frac{26}{14}q-(\frac{-45}{28}) & \text{Maak de som} \\ &=q^2+\frac{13}{7}q+\frac{45}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(\frac{7}{9}+x)(\frac{3}{8}-p)& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{-p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{8}x-\frac{7}{9}p+\frac{7}{9}.\frac{3}{8}& \text{Uitwerken } \\ & =-px+\frac{3}{8}x-\frac{7}{9}p+\frac{21}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{3}{8}x-\frac{7}{9}p+\frac{7}{24} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{17}{12})(\frac{5}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{-17}{12}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{2}p-\frac{17}{12}b-\frac{17}{12}.\frac{5}{2}& \text{Uitwerken } \\ & =bp+\frac{5}{2}p-\frac{17}{12}b-\frac{85}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{18}{6}+x)(q+\frac{-5}{13})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{13}x+3q-3.\frac{5}{13}& \text{Uitwerken } \\ & =qx-\frac{5}{13}x+3q-\frac{15}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{-14}{16})(x+\frac{2}{13})& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{x}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{13}b+\frac{7}{8}x+\frac{7}{8}.\frac{2}{13}& \text{Uitwerken } \\ & =bx+\frac{2}{13}b+\frac{7}{8}x+\frac{14}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{2}{13}b+\frac{7}{8}x+\frac{7}{52} & \text{Vereenvoudig} \\\end{align}\)