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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-10}{18})(q-\frac{14}{8})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{4}p-\frac{5}{9}q+\frac{5}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =pq-\frac{7}{4}p-\frac{5}{9}q+\frac{35}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-19}{12})(x+\frac{-19}{6})& =(\color{red}{b}+\color{orange}{\frac{19}{12}}).(\color{green}{x}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{19}{12})} . \color{green}{(x)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{6}b+\frac{19}{12}x-\frac{19}{12}.\frac{19}{6}& \text{Uitwerken } \\ & =bx-\frac{19}{6}b+\frac{19}{12}x-\frac{361}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{6}+a)(\frac{16}{7}+x)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{7}a+1x+1.\frac{16}{7}& \text{Uitwerken } \\ & =ax+\frac{16}{7}a+1x+\frac{16}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{-9}{17})(q-(-5))& =(\color{red}{b}+\color{orange}{\frac{9}{17}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{9}{17})} . \color{green}{(q)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bq+5b+\frac{9}{17}q+\frac{9}{17}.5& \text{Uitwerken } \\ & =bq+5b+\frac{9}{17}q+\frac{45}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{4}+q)(\frac{-8}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4q-\frac{5}{2}x+\frac{5}{2}.4& \text{Uitwerken } \\ & =qx-4q-\frac{5}{2}x+\frac{20}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-4q-\frac{5}{2}x+10 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{10}{6})(p+\frac{7}{13})& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{13}a+\frac{5}{3}p+\frac{5}{3}.\frac{7}{13}& \text{Uitwerken } \\ & =ap+\frac{7}{13}a+\frac{5}{3}p+\frac{35}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-18}{7})(\frac{9}{10}+a)& =(\color{red}{q}+\color{orange}{\frac{-18}{7}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{10}q-\frac{18}{7}a-\frac{18}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =aq+\frac{9}{10}q-\frac{18}{7}a-\frac{162}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{9}{10}q-\frac{18}{7}a-\frac{81}{35} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{15}{13}-b)(q+\frac{-12}{4})& =(\color{red}{-b}+\color{orange}{\frac{15}{13}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(\frac{15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bq+3b+\frac{15}{13}q-\frac{15}{13}.3& \text{Uitwerken } \\ & =-bq+3b+\frac{15}{13}q-\frac{45}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{20}{3}+q)(a-\frac{12}{17})& =(\color{red}{q}+\color{orange}{\frac{20}{3}}).(\color{green}{a}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{20}{3})} . \color{green}{(a)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{12}{17}q+\frac{20}{3}a-\frac{20}{3}.\frac{12}{17}& \text{Uitwerken } \\ & =aq-\frac{12}{17}q+\frac{20}{3}a-\frac{240}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{12}{17}q+\frac{20}{3}a-\frac{80}{17} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{-9}{12})(\frac{2}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}p+\frac{3}{4}x+\frac{3}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}p+\frac{3}{4}x+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{-10}{19})(\frac{-14}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{-10}{19}}).(\color{green}{x}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{19}b-\frac{10}{19}x+\frac{10}{19}.\frac{14}{19}& \text{Uitwerken } \\ & =bx-\frac{14}{19}b-\frac{10}{19}x+\frac{140}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{5}-x)(\frac{-5}{12}-p)& =(\color{red}{-x}+\color{orange}{\frac{-19}{5}}).(\color{green}{-p}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{12}x+\frac{19}{5}p+\frac{19}{5}.\frac{5}{12}& \text{Uitwerken } \\ & =px+\frac{5}{12}x+\frac{19}{5}p+\frac{95}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{12}x+\frac{19}{5}p+\frac{19}{12} & \text{Vereenvoudig} \\\end{align}\)