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

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Werk uit en vereenvoudig

1. \((\frac{3}{9}+x)(\frac{-17}{15}+p)\)
2. \((b+\frac{8}{15})(q+\frac{5}{7})\)
3. \((q-\frac{4}{16})(p-\frac{9}{19})\)
4. \((a-1)(p-\frac{18}{14})\)
5. \((q+\frac{18}{5})(\frac{-12}{2}+x)\)
6. \((b-\frac{8}{17})(q+\frac{16}{11})\)
7. \((\frac{-11}{5}-x)(\frac{-19}{6}+q)\)
8. \((q-\frac{-12}{5})(b-\frac{-2}{9})\)
9. \((a-\frac{-13}{15})(\frac{-20}{10}-b)\)
10. \((\frac{-10}{5}+x)(\frac{12}{2}-b)\)
11. \((a-\frac{-18}{15})(\frac{9}{13}-x)\)
12. \((\frac{-5}{14}-a)(\frac{2}{15}+p)\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{3}{9}+x)(\frac{-17}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{15}x+\frac{1}{3}p-\frac{1}{3}.\frac{17}{15}& \text{Uitwerken } \\ & =px-\frac{17}{15}x+\frac{1}{3}p-\frac{17}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{8}{15})(q+\frac{5}{7})& =(\color{red}{b}+\color{orange}{\frac{8}{15}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{7}b+\frac{8}{15}q+\frac{8}{15}.\frac{5}{7}& \text{Uitwerken } \\ & =bq+\frac{5}{7}b+\frac{8}{15}q+\frac{40}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{7}b+\frac{8}{15}q+\frac{8}{21} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{4}{16})(p-\frac{9}{19})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{19}q-\frac{1}{4}p+\frac{1}{4}.\frac{9}{19}& \text{Uitwerken } \\ & =pq-\frac{9}{19}q-\frac{1}{4}p+\frac{9}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-1)(p-\frac{18}{14})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{7}a-1p+1.\frac{9}{7}& \text{Uitwerken } \\ & =ap-\frac{9}{7}a-1p+\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{18}{5})(\frac{-12}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{18}{5}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = qx-6q+\frac{18}{5}x-\frac{18}{5}.6& \text{Uitwerken } \\ & =qx-6q+\frac{18}{5}x-\frac{108}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{8}{17})(q+\frac{16}{11})& =(\color{red}{b}+\color{orange}{\frac{-8}{17}}).(\color{green}{q}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{11}b-\frac{8}{17}q-\frac{8}{17}.\frac{16}{11}& \text{Uitwerken } \\ & =bq+\frac{16}{11}b-\frac{8}{17}q-\frac{128}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{5}-x)(\frac{-19}{6}+q)& =(\color{red}{-x}+\color{orange}{\frac{-11}{5}}).(\color{green}{q}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{6}x-\frac{11}{5}q+\frac{11}{5}.\frac{19}{6}& \text{Uitwerken } \\ & =-qx+\frac{19}{6}x-\frac{11}{5}q+\frac{209}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q-\frac{-12}{5})(b-\frac{-2}{9})& =(\color{red}{q}+\color{orange}{\frac{12}{5}}).(\color{green}{b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{12}{5})} . \color{green}{(b)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{9}q+\frac{12}{5}b+\frac{12}{5}.\frac{2}{9}& \text{Uitwerken } \\ & =bq+\frac{2}{9}q+\frac{12}{5}b+\frac{24}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{2}{9}q+\frac{12}{5}b+\frac{8}{15} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{-13}{15})(\frac{-20}{10}-b)& =(\color{red}{a}+\color{orange}{\frac{13}{15}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{13}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab-2a-\frac{13}{15}b-\frac{13}{15}.2& \text{Uitwerken } \\ & =-ab-2a-\frac{13}{15}b-\frac{26}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{5}+x)(\frac{12}{2}-b)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{6})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -bx+6x+2b-2.6& \text{Uitwerken } \\ & =-bx+6x+2b-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-18}{15})(\frac{9}{13}-x)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-x}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{13}a-\frac{6}{5}x+\frac{6}{5}.\frac{9}{13}& \text{Uitwerken } \\ & =-ax+\frac{9}{13}a-\frac{6}{5}x+\frac{54}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{14}-a)(\frac{2}{15}+p)& =(\color{red}{-a}+\color{orange}{\frac{-5}{14}}).(\color{green}{p}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{15}a-\frac{5}{14}p-\frac{5}{14}.\frac{2}{15}& \text{Uitwerken } \\ & =-ap-\frac{2}{15}a-\frac{5}{14}p-\frac{10}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{2}{15}a-\frac{5}{14}p-\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)