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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{9}{17})(q+\frac{-14}{11})& =(\color{red}{b}+\color{orange}{\frac{9}{17}}).(\color{green}{q}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(\frac{9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{14}{11}b+\frac{9}{17}q-\frac{9}{17}.\frac{14}{11}& \text{Uitwerken } \\ & =bq-\frac{14}{11}b+\frac{9}{17}q-\frac{126}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{1}{11}+b)(\frac{-14}{20}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{q}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{10}b+\frac{1}{11}q-\frac{1}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =bq-\frac{7}{10}b+\frac{1}{11}q-\frac{7}{110} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{15}{19}+p)(q+\frac{-1}{14})& =(\color{red}{p}+\color{orange}{\frac{15}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{14}p+\frac{15}{19}q-\frac{15}{19}.\frac{1}{14}& \text{Uitwerken } \\ & =pq-\frac{1}{14}p+\frac{15}{19}q-\frac{15}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{-12}{10})(p-\frac{7}{11})& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{p}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{11}x-\frac{6}{5}p+\frac{6}{5}.\frac{7}{11}& \text{Uitwerken } \\ & =px-\frac{7}{11}x-\frac{6}{5}p+\frac{42}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-5}{20})(a+\frac{-7}{15})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{15}x+\frac{1}{4}a-\frac{1}{4}.\frac{7}{15}& \text{Uitwerken } \\ & =ax-\frac{7}{15}x+\frac{1}{4}a-\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{14}{13})(a+\frac{14}{4})& =(\color{red}{a}+\color{orange}{\frac{14}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{14}{13})} . \color{green}{(a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{2}a+\frac{14}{13}a+\frac{14}{13}.\frac{7}{2}& \text{Uitwerken } \\ & =a^2+(\frac{7}{2}+\frac{14}{13})a+\frac{98}{26} & \text{Neem samen} \\ &=a^2+\frac{119}{26}a+\frac{98}{26} & \text{Maak de som} \\ &=a^2+\frac{119}{26}a+\frac{49}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{9}-q)(1+p)& =(\color{red}{-q}+\color{orange}{\frac{-11}{9}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1q-\frac{11}{9}p-\frac{11}{9}.1& \text{Uitwerken } \\ & =-pq-1q-\frac{11}{9}p-\frac{11}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-5}{2}-b)(\frac{-5}{20}-b)& =(\color{red}{-b}+\color{orange}{\frac{-5}{2}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{4}b+\frac{5}{2}b+\frac{5}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =b^2+(\frac{1}{4}+\frac{5}{2})b+\frac{5}{8} & \text{Neem samen} \\ &=b^2+\frac{11}{4}b+\frac{5}{8} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{2}{18}-q)(\frac{2}{3}-a)& =(\color{red}{-q}+\color{orange}{\frac{1}{9}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{3}q-\frac{1}{9}a+\frac{1}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =aq-\frac{2}{3}q-\frac{1}{9}a+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{10}{15}-b)(\frac{2}{11}+p)& =(\color{red}{-b}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{11}b+\frac{2}{3}p+\frac{2}{3}.\frac{2}{11}& \text{Uitwerken } \\ & =-bp-\frac{2}{11}b+\frac{2}{3}p+\frac{4}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{12}{6})(x-\frac{-11}{15})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{15}p-2x-2.\frac{11}{15}& \text{Uitwerken } \\ & =px+\frac{11}{15}p-2x-\frac{22}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{20}{7}+x)(q+\frac{12}{17})& =(\color{red}{x}+\color{orange}{\frac{20}{7}}).(\color{green}{q}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{20}{7})} . \color{green}{(q)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{17}x+\frac{20}{7}q+\frac{20}{7}.\frac{12}{17}& \text{Uitwerken } \\ & =qx+\frac{12}{17}x+\frac{20}{7}q+\frac{240}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)