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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(3+b)(\frac{16}{12}-b)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{4}{3}b-3b+3.\frac{4}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{4}{3}+(-3))b+(\frac{-12}{3}) & \text{Neem samen} \\ &=-b^2-\frac{5}{3}b+(\frac{-12}{3}) & \text{Maak de som} \\ &=-b^2-\frac{5}{3}b+(-4) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(\frac{1}{14}-a)(\frac{-6}{9}+x)& =(\color{red}{-a}+\color{orange}{\frac{1}{14}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{3}a+\frac{1}{14}x-\frac{1}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax+\frac{2}{3}a+\frac{1}{14}x-\frac{2}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{2}{3}a+\frac{1}{14}x-\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{15}{9}+p)(q+\frac{12}{9})& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}p+\frac{5}{3}q+\frac{5}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}p+\frac{5}{3}q+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-14}{18})(x+\frac{-18}{10})& =(\color{red}{q}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{9}{5}q+\frac{7}{9}x-\frac{7}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =qx-\frac{9}{5}q+\frac{7}{9}x-\frac{63}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{9}{5}q+\frac{7}{9}x-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{11}{15})(\frac{-8}{5}-x)& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{-x}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{5}p+\frac{11}{15}x+\frac{11}{15}.\frac{8}{5}& \text{Uitwerken } \\ & =-px-\frac{8}{5}p+\frac{11}{15}x+\frac{88}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{3}{15}-b)(\frac{-7}{14}+q)& =(\color{red}{-b}+\color{orange}{\frac{1}{5}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{2}b+\frac{1}{5}q-\frac{1}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-bq+\frac{1}{2}b+\frac{1}{5}q-\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{16}{12}+x)(\frac{-4}{18}-p)& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{-p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{9}x-\frac{4}{3}p-\frac{4}{3}.\frac{2}{9}& \text{Uitwerken } \\ & =-px-\frac{2}{9}x-\frac{4}{3}p-\frac{8}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{3}{10})(a+\frac{3}{14})& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{14}p-\frac{3}{10}a-\frac{3}{10}.\frac{3}{14}& \text{Uitwerken } \\ & =ap+\frac{3}{14}p-\frac{3}{10}a-\frac{9}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{1}{12})(\frac{1}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{12}}).(\color{green}{-q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{4}a+\frac{1}{12}q-\frac{1}{12}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq+\frac{1}{4}a+\frac{1}{12}q-\frac{1}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-14}{11}+b)(\frac{5}{9}-p)& =(\color{red}{b}+\color{orange}{\frac{-14}{11}}).(\color{green}{-p}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{9}b+\frac{14}{11}p-\frac{14}{11}.\frac{5}{9}& \text{Uitwerken } \\ & =-bp+\frac{5}{9}b+\frac{14}{11}p-\frac{70}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-12}{17}+a)(x-\frac{13}{13})& =(\color{red}{a}+\color{orange}{\frac{-12}{17}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-12}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a-\frac{12}{17}x+\frac{12}{17}.1& \text{Uitwerken } \\ & =ax-1a-\frac{12}{17}x+\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-17}{8})(a-\frac{-16}{9})& =(\color{red}{p}+\color{orange}{\frac{-17}{8}}).(\color{green}{a}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{9}p-\frac{17}{8}a-\frac{17}{8}.\frac{16}{9}& \text{Uitwerken } \\ & =ap+\frac{16}{9}p-\frac{17}{8}a-\frac{272}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{16}{9}p-\frac{17}{8}a-\frac{34}{9} & \text{Vereenvoudig} \\\end{align}\)