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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{16}+a)(\frac{-13}{6}+x)& =(\color{red}{a}+\color{orange}{\frac{15}{16}}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{15}{16})} . \color{green}{(x)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{6}a+\frac{15}{16}x-\frac{15}{16}.\frac{13}{6}& \text{Uitwerken } \\ & =ax-\frac{13}{6}a+\frac{15}{16}x-\frac{195}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{13}{6}a+\frac{15}{16}x-\frac{65}{32} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a+\frac{9}{6})(x+\frac{11}{4})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{4})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{11}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{4}a+\frac{3}{2}x+\frac{3}{2}.\frac{11}{4}& \text{Uitwerken } \\ & =ax+\frac{11}{4}a+\frac{3}{2}x+\frac{33}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-11}{2}+a)(x+\frac{17}{12})& =(\color{red}{a}+\color{orange}{\frac{-11}{2}}).(\color{green}{x}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{12}a-\frac{11}{2}x-\frac{11}{2}.\frac{17}{12}& \text{Uitwerken } \\ & =ax+\frac{17}{12}a-\frac{11}{2}x-\frac{187}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{4}{17})(\frac{4}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{-4}{17}}).(\color{green}{-p}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{7}x+\frac{4}{17}p-\frac{4}{17}.\frac{2}{7}& \text{Uitwerken } \\ & =-px+\frac{2}{7}x+\frac{4}{17}p-\frac{8}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{14}{8})(b-\frac{-11}{6})& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{6}p-\frac{7}{4}b-\frac{7}{4}.\frac{11}{6}& \text{Uitwerken } \\ & =bp+\frac{11}{6}p-\frac{7}{4}b-\frac{77}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+1)(q+\frac{15}{17})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{17}a+1q+1.\frac{15}{17}& \text{Uitwerken } \\ & =aq+\frac{15}{17}a+1q+\frac{15}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{17}{6}-a)(b+\frac{2}{8})& =(\color{red}{-a}+\color{orange}{\frac{17}{6}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{4}a+\frac{17}{6}b+\frac{17}{6}.\frac{1}{4}& \text{Uitwerken } \\ & =-ab-\frac{1}{4}a+\frac{17}{6}b+\frac{17}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{5}{13}+x)(\frac{17}{3}-a)& =(\color{red}{x}+\color{orange}{\frac{5}{13}}).(\color{green}{-a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{5}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{3}x-\frac{5}{13}a+\frac{5}{13}.\frac{17}{3}& \text{Uitwerken } \\ & =-ax+\frac{17}{3}x-\frac{5}{13}a+\frac{85}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{17}+a)(\frac{7}{16}+q)& =(\color{red}{a}+\color{orange}{\frac{-20}{17}}).(\color{green}{q}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{16}a-\frac{20}{17}q-\frac{20}{17}.\frac{7}{16}& \text{Uitwerken } \\ & =aq+\frac{7}{16}a-\frac{20}{17}q-\frac{140}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{16}a-\frac{20}{17}q-\frac{35}{68} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{9}{8}-b)(\frac{3}{9}+b)& =(\color{red}{-b}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{3}b+\frac{9}{8}b+\frac{9}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{3})+\frac{9}{8})b+(\frac{-9}{24}) & \text{Neem samen} \\ &=-b^2+\frac{19}{24}b+(\frac{-9}{24}) & \text{Maak de som} \\ &=-b^2+\frac{19}{24}b+(\frac{-3}{8}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{17}+q)(\frac{14}{8}+q)& =(\color{red}{q}+\color{orange}{\frac{-9}{17}}).(\color{green}{q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{4}q-\frac{9}{17}q-\frac{9}{17}.\frac{7}{4}& \text{Uitwerken } \\ & =q^2+(\frac{7}{4}+(\frac{-9}{17}))q-(\frac{-63}{68}) & \text{Neem samen} \\ &=q^2+\frac{83}{68}q-(\frac{-63}{68}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{16}{7}+a)(p-\frac{4}{12})& =(\color{red}{a}+\color{orange}{\frac{16}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{3}a+\frac{16}{7}p-\frac{16}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =ap-\frac{1}{3}a+\frac{16}{7}p-\frac{16}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)