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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{4}{7}-a)(\frac{3}{11}+q)& =(\color{red}{-a}+\color{orange}{\frac{4}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{11}a+\frac{4}{7}q+\frac{4}{7}.\frac{3}{11}& \text{Uitwerken } \\ & =-aq-\frac{3}{11}a+\frac{4}{7}q+\frac{12}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{16}{4})(q-\frac{-6}{13})& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{6}{13}b-4q-4.\frac{6}{13}& \text{Uitwerken } \\ & =bq+\frac{6}{13}b-4q-\frac{24}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{6}{9})(p-\frac{-20}{3})& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{3}x+\frac{2}{3}p+\frac{2}{3}.\frac{20}{3}& \text{Uitwerken } \\ & =px+\frac{20}{3}x+\frac{2}{3}p+\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{15}-a)(\frac{-20}{10}-a)& =(\color{red}{-a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a+\frac{3}{5}a+\frac{3}{5}.2& \text{Uitwerken } \\ & =a^2+(2+\frac{3}{5})a+\frac{6}{5} & \text{Neem samen} \\ &=a^2+\frac{13}{5}a+\frac{6}{5} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(p-\frac{-13}{9})(p-\frac{7}{19})& =(\color{red}{p}+\color{orange}{\frac{13}{9}}).(\color{green}{p}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{13}{9})} . \color{green}{(p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{19}p+\frac{13}{9}p-\frac{13}{9}.\frac{7}{19}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{19})+\frac{13}{9})p-(\frac{-91}{171}) & \text{Neem samen} \\ &=p^2+\frac{184}{171}p-(\frac{-91}{171}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(p-\frac{-13}{11})(q-\frac{-14}{7})& =(\color{red}{p}+\color{orange}{\frac{13}{11}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{13}{11})} . \color{green}{(q)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p+\frac{13}{11}q+\frac{13}{11}.2& \text{Uitwerken } \\ & =pq+2p+\frac{13}{11}q+\frac{26}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{17}+q)(p+\frac{10}{20})& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}q+\frac{7}{17}p+\frac{7}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}q+\frac{7}{17}p+\frac{7}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{17}{4})(x+\frac{-17}{12})& =(\color{red}{p}+\color{orange}{\frac{17}{4}}).(\color{green}{x}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{12}p+\frac{17}{4}x-\frac{17}{4}.\frac{17}{12}& \text{Uitwerken } \\ & =px-\frac{17}{12}p+\frac{17}{4}x-\frac{289}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-14}{17})(\frac{-11}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{-14}{17}}).(\color{green}{a}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{15}b-\frac{14}{17}a+\frac{14}{17}.\frac{11}{15}& \text{Uitwerken } \\ & =ab-\frac{11}{15}b-\frac{14}{17}a+\frac{154}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{12}{6}+a)(\frac{11}{14}+x)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{14}a+2x+2.\frac{11}{14}& \text{Uitwerken } \\ & =ax+\frac{11}{14}a+2x+\frac{22}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{14}a+2x+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-5}{5}+a)(q-\frac{-7}{7})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1a-1q-1.1& \text{Uitwerken } \\ & =aq+1a-1q-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{11}-x)(\frac{-2}{8}-q)& =(\color{red}{-x}+\color{orange}{\frac{-15}{11}}).(\color{green}{-q}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}x+\frac{15}{11}q+\frac{15}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}x+\frac{15}{11}q+\frac{15}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)