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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{2}{12}-q)(x+\frac{18}{18})& =(\color{red}{-q}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1q+\frac{1}{6}x+\frac{1}{6}.1& \text{Uitwerken } \\ & =-qx-1q+\frac{1}{6}x+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{12}{4}+b)(q+\frac{-20}{11})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{20}{11}b+3q-3.\frac{20}{11}& \text{Uitwerken } \\ & =bq-\frac{20}{11}b+3q-\frac{60}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{20}+p)(x-\frac{19}{20})& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{20}p+\frac{3}{10}x-\frac{3}{10}.\frac{19}{20}& \text{Uitwerken } \\ & =px-\frac{19}{20}p+\frac{3}{10}x-\frac{57}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{7}{7}-x)(b-\frac{15}{2})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{2}x+1b-1.\frac{15}{2}& \text{Uitwerken } \\ & =-bx+\frac{15}{2}x+1b-\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{18}+a)(\frac{1}{17}+a)& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{17}a-\frac{2}{9}a-\frac{2}{9}.\frac{1}{17}& \text{Uitwerken } \\ & =a^2+(\frac{1}{17}+(\frac{-2}{9}))a-(\frac{-2}{153}) & \text{Neem samen} \\ &=a^2-\frac{25}{153}a-(\frac{-2}{153}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-1}{10}-x)(b+\frac{-17}{13})& =(\color{red}{-x}+\color{orange}{\frac{-1}{10}}).(\color{green}{b}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{13}x-\frac{1}{10}b+\frac{1}{10}.\frac{17}{13}& \text{Uitwerken } \\ & =-bx+\frac{17}{13}x-\frac{1}{10}b+\frac{17}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-2}{5}+b)(\frac{-4}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{5}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1b-\frac{2}{5}p+\frac{2}{5}.1& \text{Uitwerken } \\ & =bp-1b-\frac{2}{5}p+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{13}+a)(\frac{-6}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{3}{13}}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{3}{13})} . \color{green}{(q)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{13}a+\frac{3}{13}q-\frac{3}{13}.\frac{6}{13}& \text{Uitwerken } \\ & =aq-\frac{6}{13}a+\frac{3}{13}q-\frac{18}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{-15}{3})(b-\frac{7}{13})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{13}x+5b-5.\frac{7}{13}& \text{Uitwerken } \\ & =bx-\frac{7}{13}x+5b-\frac{35}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-1}{10}+a)(a-\frac{-1}{20})& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{20}a-\frac{1}{10}a-\frac{1}{10}.\frac{1}{20}& \text{Uitwerken } \\ & =a^2+(\frac{1}{20}+(\frac{-1}{10}))a-(\frac{-1}{200}) & \text{Neem samen} \\ &=a^2-\frac{1}{20}a-(\frac{-1}{200}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(p-\frac{-20}{12})(q-\frac{-5}{9})& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{9}p+\frac{5}{3}q+\frac{5}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =pq+\frac{5}{9}p+\frac{5}{3}q+\frac{25}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{19}{15})(b-\frac{17}{13})& =(\color{red}{b}+\color{orange}{\frac{-19}{15}}).(\color{green}{b}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{13}b-\frac{19}{15}b+\frac{19}{15}.\frac{17}{13}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{13})+(\frac{-19}{15}))b+\frac{323}{195} & \text{Neem samen} \\ &=b^2-\frac{502}{195}b+\frac{323}{195} & \text{Maak de som} \\\end{align}\)