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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-8}{15})(\frac{-16}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-8}{15}}).(\color{green}{-x}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-8}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax-4a+\frac{8}{15}x+\frac{8}{15}.4& \text{Uitwerken } \\ & =-ax-4a+\frac{8}{15}x+\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{5}{8})(q-\frac{11}{14})& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{q}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{5}{8})} . \color{green}{(q)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{14}a+\frac{5}{8}q-\frac{5}{8}.\frac{11}{14}& \text{Uitwerken } \\ & =aq-\frac{11}{14}a+\frac{5}{8}q-\frac{55}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{14}{3}-q)(\frac{1}{4}-b)& =(\color{red}{-q}+\color{orange}{\frac{14}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{14}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{4}q-\frac{14}{3}b+\frac{14}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =bq-\frac{1}{4}q-\frac{14}{3}b+\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{4}q-\frac{14}{3}b+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{-18}{14})(q-\frac{-2}{8})& =(\color{red}{p}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{4}p-\frac{9}{7}q-\frac{9}{7}.\frac{1}{4}& \text{Uitwerken } \\ & =pq+\frac{1}{4}p-\frac{9}{7}q-\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{19}{18}+b)(x+\frac{12}{16})& =(\color{red}{b}+\color{orange}{\frac{19}{18}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b+\frac{19}{18}x+\frac{19}{18}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b+\frac{19}{18}x+\frac{57}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{4}b+\frac{19}{18}x+\frac{19}{24} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{-20}{16})(\frac{11}{17}-x)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{-x}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{17}a+\frac{5}{4}x-\frac{5}{4}.\frac{11}{17}& \text{Uitwerken } \\ & =-ax+\frac{11}{17}a+\frac{5}{4}x-\frac{55}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{1}{4}+q)(\frac{-13}{20}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{20}q-\frac{1}{4}b-\frac{1}{4}.\frac{13}{20}& \text{Uitwerken } \\ & =-bq-\frac{13}{20}q-\frac{1}{4}b-\frac{13}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-9}{5})(q+\frac{-6}{16})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{8}b-\frac{9}{5}q+\frac{9}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =bq-\frac{3}{8}b-\frac{9}{5}q+\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{17}{6})(\frac{3}{12}-p)& =(\color{red}{a}+\color{orange}{\frac{17}{6}}).(\color{green}{-p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{4}a-\frac{17}{6}p+\frac{17}{6}.\frac{1}{4}& \text{Uitwerken } \\ & =-ap+\frac{1}{4}a-\frac{17}{6}p+\frac{17}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{16}{6})(p+\frac{2}{2})& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q+\frac{8}{3}p+\frac{8}{3}.1& \text{Uitwerken } \\ & =pq+1q+\frac{8}{3}p+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{18}{4}-q)(x-\frac{-8}{17})& =(\color{red}{-q}+\color{orange}{\frac{9}{2}}).(\color{green}{x}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{17}q+\frac{9}{2}x+\frac{9}{2}.\frac{8}{17}& \text{Uitwerken } \\ & =-qx-\frac{8}{17}q+\frac{9}{2}x+\frac{72}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{8}{17}q+\frac{9}{2}x+\frac{36}{17} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-10}{7}-b)(p+\frac{-10}{5})& =(\color{red}{-b}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2b-\frac{10}{7}p+\frac{10}{7}.2& \text{Uitwerken } \\ & =-bp+2b-\frac{10}{7}p+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)