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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{14}{16}-a)(\frac{-5}{7}+p)& =(\color{red}{-a}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{7}a+\frac{7}{8}p-\frac{7}{8}.\frac{5}{7}& \text{Uitwerken } \\ & =-ap+\frac{5}{7}a+\frac{7}{8}p-\frac{35}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{5}{7}a+\frac{7}{8}p-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-11}{7}+x)(\frac{-4}{8}-p)& =(\color{red}{x}+\color{orange}{\frac{-11}{7}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{2}x+\frac{11}{7}p+\frac{11}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-px-\frac{1}{2}x+\frac{11}{7}p+\frac{11}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{15}{14})(a-\frac{19}{14})& =(\color{red}{p}+\color{orange}{\frac{15}{14}}).(\color{green}{a}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{14}p+\frac{15}{14}a-\frac{15}{14}.\frac{19}{14}& \text{Uitwerken } \\ & =ap-\frac{19}{14}p+\frac{15}{14}a-\frac{285}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-5}{7})(q+\frac{11}{8})& =(\color{red}{x}+\color{orange}{\frac{5}{7}}).(\color{green}{q}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{8}x+\frac{5}{7}q+\frac{5}{7}.\frac{11}{8}& \text{Uitwerken } \\ & =qx+\frac{11}{8}x+\frac{5}{7}q+\frac{55}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{13}-a)(\frac{-3}{2}-q)& =(\color{red}{-a}+\color{orange}{\frac{6}{13}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{6}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}a-\frac{6}{13}q-\frac{6}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}a-\frac{6}{13}q-\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{2}a-\frac{6}{13}q-\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{-1}{18})(q-\frac{16}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{18}}).(\color{green}{q}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{1}{18})} . \color{green}{(q)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{7}x+\frac{1}{18}q-\frac{1}{18}.\frac{16}{7}& \text{Uitwerken } \\ & =qx-\frac{16}{7}x+\frac{1}{18}q-\frac{16}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{16}{7}x+\frac{1}{18}q-\frac{8}{63} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{13}{4}-p)(q+\frac{19}{20})& =(\color{red}{-p}+\color{orange}{\frac{13}{4}}).(\color{green}{q}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{20}p+\frac{13}{4}q+\frac{13}{4}.\frac{19}{20}& \text{Uitwerken } \\ & =-pq-\frac{19}{20}p+\frac{13}{4}q+\frac{247}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{15}{16})(\frac{-6}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{15}{16}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2a+\frac{15}{16}p-\frac{15}{16}.2& \text{Uitwerken } \\ & =ap-2a+\frac{15}{16}p-\frac{30}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-2a+\frac{15}{16}p-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{7}{3})(p-\frac{-17}{18})& =(\color{red}{x}+\color{orange}{\frac{-7}{3}}).(\color{green}{p}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{18}x-\frac{7}{3}p-\frac{7}{3}.\frac{17}{18}& \text{Uitwerken } \\ & =px+\frac{17}{18}x-\frac{7}{3}p-\frac{119}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+\frac{-11}{12})(\frac{10}{5}+b)& =(\color{red}{b}+\color{orange}{\frac{-11}{12}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b-\frac{11}{12}b-\frac{11}{12}.2& \text{Uitwerken } \\ & =b^2+(2+(\frac{-11}{12}))b-(\frac{-22}{12}) & \text{Neem samen} \\ &=b^2+\frac{13}{12}b-(\frac{-22}{12}) & \text{Maak de som} \\ &=b^2+\frac{13}{12}b+\frac{11}{6} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
11. \(\begin{align}(\frac{-11}{12}+b)(\frac{-4}{13}-b)& =(\color{red}{b}+\color{orange}{\frac{-11}{12}}).(\color{green}{-b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{13}b+\frac{11}{12}b+\frac{11}{12}.\frac{4}{13}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{13})+\frac{11}{12})b+(\frac{-44}{156}) & \text{Neem samen} \\ &=-b^2+\frac{95}{156}b+(\frac{-44}{156}) & \text{Maak de som} \\ &=-b^2+\frac{95}{156}b+(\frac{-11}{39}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(x+\frac{1}{4})(p-\frac{-7}{13})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{13}x+\frac{1}{4}p+\frac{1}{4}.\frac{7}{13}& \text{Uitwerken } \\ & =px+\frac{7}{13}x+\frac{1}{4}p+\frac{7}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)