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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{3}{13})(\frac{-3}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{13}}).(\color{green}{-x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{3}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{8}a-\frac{3}{13}x-\frac{3}{13}.\frac{3}{8}& \text{Uitwerken } \\ & =-ax-\frac{3}{8}a-\frac{3}{13}x-\frac{9}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{13}{19})(p-\frac{10}{18})& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{13}{19})} . \color{green}{(p)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{9}q+\frac{13}{19}p-\frac{13}{19}.\frac{5}{9}& \text{Uitwerken } \\ & =pq-\frac{5}{9}q+\frac{13}{19}p-\frac{65}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{14}-b)(q-\frac{-4}{4})& =(\color{red}{-b}+\color{orange}{\frac{-19}{14}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1b-\frac{19}{14}q-\frac{19}{14}.1& \text{Uitwerken } \\ & =-bq-1b-\frac{19}{14}q-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{8}{6})(\frac{1}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{18}a-\frac{4}{3}q-\frac{4}{3}.\frac{1}{18}& \text{Uitwerken } \\ & =aq+\frac{1}{18}a-\frac{4}{3}q-\frac{4}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{18}a-\frac{4}{3}q-\frac{2}{27} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{12}+p)(a-\frac{-7}{8})& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{8}p-\frac{5}{6}a-\frac{5}{6}.\frac{7}{8}& \text{Uitwerken } \\ & =ap+\frac{7}{8}p-\frac{5}{6}a-\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{7}{19})(x-\frac{20}{20})& =(\color{red}{a}+\color{orange}{\frac{7}{19}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{19})} . \color{green}{(x)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{7}{19}x-\frac{7}{19}.1& \text{Uitwerken } \\ & =ax-1a+\frac{7}{19}x-\frac{7}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-13}{20}-p)(\frac{-20}{20}-q)& =(\color{red}{-p}+\color{orange}{\frac{-13}{20}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p+\frac{13}{20}q+\frac{13}{20}.1& \text{Uitwerken } \\ & =pq+1p+\frac{13}{20}q+\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-11}{5}-x)(x+\frac{-14}{17})& =(\color{red}{-x}+\color{orange}{\frac{-11}{5}}).(\color{green}{x}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{14}{17}x-\frac{11}{5}x+\frac{11}{5}.\frac{14}{17}& \text{Uitwerken } \\ & =-x^2+(\frac{14}{17}+(\frac{-11}{5}))x+(\frac{-154}{85}) & \text{Neem samen} \\ &=-x^2-\frac{117}{85}x+(\frac{-154}{85}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(b-\frac{12}{13})(q-\frac{-12}{9})& =(\color{red}{b}+\color{orange}{\frac{-12}{13}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{3}b-\frac{12}{13}q-\frac{12}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =bq+\frac{4}{3}b-\frac{12}{13}q-\frac{48}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{4}{3}b-\frac{12}{13}q-\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{18}{14})(\frac{-16}{12}-q)& =(\color{red}{a}+\color{orange}{\frac{-9}{7}}).(\color{green}{-q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{4}{3}a+\frac{9}{7}q+\frac{9}{7}.\frac{4}{3}& \text{Uitwerken } \\ & =-aq-\frac{4}{3}a+\frac{9}{7}q+\frac{36}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{4}{3}a+\frac{9}{7}q+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x+\frac{-14}{10})(a-\frac{11}{2})& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{2}x-\frac{7}{5}a+\frac{7}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =ax-\frac{11}{2}x-\frac{7}{5}a+\frac{77}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{11}{19}-p)(\frac{-11}{19}+q)& =(\color{red}{-p}+\color{orange}{\frac{11}{19}}).(\color{green}{q}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{19}p+\frac{11}{19}q-\frac{11}{19}.\frac{11}{19}& \text{Uitwerken } \\ & =-pq+\frac{11}{19}p+\frac{11}{19}q-\frac{121}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)