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

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Werk uit en vereenvoudig

1. \((\frac{-19}{19}+x)(\frac{-12}{18}+q)\)
2. \((q-\frac{2}{19})(\frac{7}{16}-p)\)
3. \((\frac{12}{13}-b)(\frac{3}{10}-a)\)
4. \((\frac{18}{9}+b)(\frac{-10}{11}+q)\)
5. \((x-\frac{-20}{3})(\frac{15}{2}-b)\)
6. \((q+\frac{17}{11})(x+\frac{-12}{2})\)
7. \((\frac{10}{5}-q)(p+\frac{7}{10})\)
8. \(((-20)+b)(\frac{-20}{2}+q)\)
9. \((\frac{-11}{5}-p)(\frac{-17}{9}+a)\)
10. \((\frac{-18}{12}+q)(a+\frac{-7}{15})\)
11. \((a+\frac{-13}{18})(b+\frac{5}{7})\)
12. \((x-\frac{17}{19})(a+\frac{-12}{6})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{19}+x)(\frac{-12}{18}+q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{3}x-1q+1.\frac{2}{3}& \text{Uitwerken } \\ & =qx-\frac{2}{3}x-1q+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{2}{19})(\frac{7}{16}-p)& =(\color{red}{q}+\color{orange}{\frac{-2}{19}}).(\color{green}{-p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{-2}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{16}q+\frac{2}{19}p-\frac{2}{19}.\frac{7}{16}& \text{Uitwerken } \\ & =-pq+\frac{7}{16}q+\frac{2}{19}p-\frac{14}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{7}{16}q+\frac{2}{19}p-\frac{7}{152} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{12}{13}-b)(\frac{3}{10}-a)& =(\color{red}{-b}+\color{orange}{\frac{12}{13}}).(\color{green}{-a}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{12}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{13})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{10}b-\frac{12}{13}a+\frac{12}{13}.\frac{3}{10}& \text{Uitwerken } \\ & =ab-\frac{3}{10}b-\frac{12}{13}a+\frac{36}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{3}{10}b-\frac{12}{13}a+\frac{18}{65} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{18}{9}+b)(\frac{-10}{11}+q)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{10}{11}b+2q-2.\frac{10}{11}& \text{Uitwerken } \\ & =bq-\frac{10}{11}b+2q-\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-20}{3})(\frac{15}{2}-b)& =(\color{red}{x}+\color{orange}{\frac{20}{3}}).(\color{green}{-b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{20}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{2}x-\frac{20}{3}b+\frac{20}{3}.\frac{15}{2}& \text{Uitwerken } \\ & =-bx+\frac{15}{2}x-\frac{20}{3}b+\frac{300}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{15}{2}x-\frac{20}{3}b+50 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{17}{11})(x+\frac{-12}{2})& =(\color{red}{q}+\color{orange}{\frac{17}{11}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = qx-6q+\frac{17}{11}x-\frac{17}{11}.6& \text{Uitwerken } \\ & =qx-6q+\frac{17}{11}x-\frac{102}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{10}{5}-q)(p+\frac{7}{10})& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{7}{10}q+2p+2.\frac{7}{10}& \text{Uitwerken } \\ & =-pq-\frac{7}{10}q+2p+\frac{14}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{7}{10}q+2p+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}((-20)+b)(\frac{-20}{2}+q)& =(\color{red}{b}+\color{orange}{(-20)}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-10)} + \color{orange}{(-20)} . \color{green}{(q)} + \color{orange}{(-20)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = bq-10b-20q+20.10& \text{Uitwerken } \\ & =bq-10b-20q+200 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-11}{5}-p)(\frac{-17}{9}+a)& =(\color{red}{-p}+\color{orange}{\frac{-11}{5}}).(\color{green}{a}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{9}p-\frac{11}{5}a+\frac{11}{5}.\frac{17}{9}& \text{Uitwerken } \\ & =-ap+\frac{17}{9}p-\frac{11}{5}a+\frac{187}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-18}{12}+q)(a+\frac{-7}{15})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{15}q-\frac{3}{2}a+\frac{3}{2}.\frac{7}{15}& \text{Uitwerken } \\ & =aq-\frac{7}{15}q-\frac{3}{2}a+\frac{21}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{15}q-\frac{3}{2}a+\frac{7}{10} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{-13}{18})(b+\frac{5}{7})& =(\color{red}{a}+\color{orange}{\frac{-13}{18}}).(\color{green}{b}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{7}a-\frac{13}{18}b-\frac{13}{18}.\frac{5}{7}& \text{Uitwerken } \\ & =ab+\frac{5}{7}a-\frac{13}{18}b-\frac{65}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{17}{19})(a+\frac{-12}{6})& =(\color{red}{x}+\color{orange}{\frac{-17}{19}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-17}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax-2x-\frac{17}{19}a+\frac{17}{19}.2& \text{Uitwerken } \\ & =ax-2x-\frac{17}{19}a+\frac{34}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)