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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{14}{9}+a)(b-\frac{-10}{2})& =(\color{red}{a}+\color{orange}{\frac{14}{9}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(5)} + \color{orange}{(\frac{14}{9})} . \color{green}{(b)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ab+5a+\frac{14}{9}b+\frac{14}{9}.5& \text{Uitwerken } \\ & =ab+5a+\frac{14}{9}b+\frac{70}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{3}-p)(q-\frac{13}{14})& =(\color{red}{-p}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{13}{14}p-\frac{7}{3}q+\frac{7}{3}.\frac{13}{14}& \text{Uitwerken } \\ & =-pq+\frac{13}{14}p-\frac{7}{3}q+\frac{91}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{13}{14}p-\frac{7}{3}q+\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a-\frac{20}{5})(3-b)& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(-4)} . \color{green}{(-b)} + \color{orange}{(-4)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ab+3a+4b-4.3& \text{Uitwerken } \\ & =-ab+3a+4b-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{8}{16}-a)(\frac{-12}{14}+a)& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{6}{7}a+\frac{1}{2}a-\frac{1}{2}.\frac{6}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{6}{7}+\frac{1}{2})a-\frac{6}{14} & \text{Neem samen} \\ &=-a^2+\frac{19}{14}a-\frac{6}{14} & \text{Maak de som} \\ &=-a^2+\frac{19}{14}a-\frac{3}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{11}-q)(\frac{-12}{17}+p)& =(\color{red}{-q}+\color{orange}{\frac{-2}{11}}).(\color{green}{p}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{12}{17}q-\frac{2}{11}p+\frac{2}{11}.\frac{12}{17}& \text{Uitwerken } \\ & =-pq+\frac{12}{17}q-\frac{2}{11}p+\frac{24}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{20}{7})(\frac{12}{11}-x)& =(\color{red}{q}+\color{orange}{\frac{-20}{7}}).(\color{green}{-x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{12}{11}q+\frac{20}{7}x-\frac{20}{7}.\frac{12}{11}& \text{Uitwerken } \\ & =-qx+\frac{12}{11}q+\frac{20}{7}x-\frac{240}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-13}{16})(b+\frac{17}{2})& =(\color{red}{x}+\color{orange}{\frac{-13}{16}}).(\color{green}{b}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{2}x-\frac{13}{16}b-\frac{13}{16}.\frac{17}{2}& \text{Uitwerken } \\ & =bx+\frac{17}{2}x-\frac{13}{16}b-\frac{221}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{5}{10})(\frac{1}{18}+p)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{18}q-\frac{1}{2}p-\frac{1}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =pq+\frac{1}{18}q-\frac{1}{2}p-\frac{1}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{18}-x)(\frac{2}{11}-p)& =(\color{red}{-x}+\color{orange}{\frac{7}{18}}).(\color{green}{-p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{7}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{11}x-\frac{7}{18}p+\frac{7}{18}.\frac{2}{11}& \text{Uitwerken } \\ & =px-\frac{2}{11}x-\frac{7}{18}p+\frac{14}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{11}x-\frac{7}{18}p+\frac{7}{99} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x-\frac{-16}{3})(q-\frac{5}{12})& =(\color{red}{x}+\color{orange}{\frac{16}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{16}{3})} . \color{green}{(q)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{12}x+\frac{16}{3}q-\frac{16}{3}.\frac{5}{12}& \text{Uitwerken } \\ & =qx-\frac{5}{12}x+\frac{16}{3}q-\frac{80}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{12}x+\frac{16}{3}q-\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{10}+p)((-7)-x)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{(-7)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -px-7p-\frac{4}{5}x-\frac{4}{5}.7& \text{Uitwerken } \\ & =-px-7p-\frac{4}{5}x-\frac{28}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{11}{4}+a)(q+4)& =(\color{red}{a}+\color{orange}{\frac{11}{4}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{11}{4})} . \color{green}{(q)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aq+4a+\frac{11}{4}q+\frac{11}{4}.4& \text{Uitwerken } \\ & =aq+4a+\frac{11}{4}q+\frac{44}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+4a+\frac{11}{4}q+11 & \text{Vereenvoudig} \\\end{align}\)