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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{5}{10}-a)(\frac{-9}{13}-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{13}a-\frac{1}{2}x-\frac{1}{2}.\frac{9}{13}& \text{Uitwerken } \\ & =ax+\frac{9}{13}a-\frac{1}{2}x-\frac{9}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-4}{9}+a)(\frac{-2}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{19}a-\frac{4}{9}q+\frac{4}{9}.\frac{2}{19}& \text{Uitwerken } \\ & =aq-\frac{2}{19}a-\frac{4}{9}q+\frac{8}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{10}{2})(x-\frac{4}{11})& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{11}q-5x+5.\frac{4}{11}& \text{Uitwerken } \\ & =qx-\frac{4}{11}q-5x+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{16}{4})(p-\frac{-7}{17})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{17}b+4p+4.\frac{7}{17}& \text{Uitwerken } \\ & =bp+\frac{7}{17}b+4p+\frac{28}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{20}{19})(\frac{-8}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{20}{19}}).(\color{green}{p}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{20}{19})} . \color{green}{(p)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{13}b+\frac{20}{19}p-\frac{20}{19}.\frac{8}{13}& \text{Uitwerken } \\ & =bp-\frac{8}{13}b+\frac{20}{19}p-\frac{160}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{19}{15})(x+\frac{16}{7})& =(\color{red}{a}+\color{orange}{\frac{19}{15}}).(\color{green}{x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{19}{15})} . \color{green}{(x)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{7}a+\frac{19}{15}x+\frac{19}{15}.\frac{16}{7}& \text{Uitwerken } \\ & =ax+\frac{16}{7}a+\frac{19}{15}x+\frac{304}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{15}-p)(a+\frac{17}{5})& =(\color{red}{-p}+\color{orange}{\frac{-14}{15}}).(\color{green}{a}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{5}p-\frac{14}{15}a-\frac{14}{15}.\frac{17}{5}& \text{Uitwerken } \\ & =-ap-\frac{17}{5}p-\frac{14}{15}a-\frac{238}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-11)(x+\frac{9}{10})& =(\color{red}{a}+\color{orange}{(-11)}).(\color{green}{x}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(-11)} . \color{green}{(x)} + \color{orange}{(-11)} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{10}a-11x-11.\frac{9}{10}& \text{Uitwerken } \\ & =ax+\frac{9}{10}a-11x-\frac{99}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-7}{13})(\frac{-19}{6}-p)& =(\color{red}{q}+\color{orange}{\frac{7}{13}}).(\color{green}{-p}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{7}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{6}q-\frac{7}{13}p-\frac{7}{13}.\frac{19}{6}& \text{Uitwerken } \\ & =-pq-\frac{19}{6}q-\frac{7}{13}p-\frac{133}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{-18}{12})(a-\frac{-5}{3})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}q-\frac{3}{2}a-\frac{3}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}q-\frac{3}{2}a-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{3}q-\frac{3}{2}a-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{7}{13}-p)(x-\frac{-18}{15})& =(\color{red}{-p}+\color{orange}{\frac{7}{13}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{7}{13})} . \color{green}{(x)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{5}p+\frac{7}{13}x+\frac{7}{13}.\frac{6}{5}& \text{Uitwerken } \\ & =-px-\frac{6}{5}p+\frac{7}{13}x+\frac{42}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+4)(\frac{18}{14}+q)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{7}x+4q+4.\frac{9}{7}& \text{Uitwerken } \\ & =qx+\frac{9}{7}x+4q+\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)