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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{3}{2})(q-\frac{19}{9})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{9}b+\frac{3}{2}q-\frac{3}{2}.\frac{19}{9}& \text{Uitwerken } \\ & =bq-\frac{19}{9}b+\frac{3}{2}q-\frac{57}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{19}{9}b+\frac{3}{2}q-\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{12}{8})((-9)-q)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bq-9b+\frac{3}{2}q+\frac{3}{2}.9& \text{Uitwerken } \\ & =-bq-9b+\frac{3}{2}q+\frac{27}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{2}{17}-q)(q-\frac{1}{13})& =(\color{red}{-q}+\color{orange}{\frac{2}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{2}{17})} . \color{green}{(q)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{1}{13}q+\frac{2}{17}q-\frac{2}{17}.\frac{1}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{1}{13}+\frac{2}{17})q-\frac{2}{221} & \text{Neem samen} \\ &=-q^2+\frac{43}{221}q-\frac{2}{221} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{20}{2}-p)(b-\frac{1}{12})& =(\color{red}{-p}+\color{orange}{10}).(\color{green}{b}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(10)} . \color{green}{(b)} + \color{orange}{(10)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{12}p+10b-10.\frac{1}{12}& \text{Uitwerken } \\ & =-bp+\frac{1}{12}p+10b-\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{12}p+10b-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{16}+a)(x-\frac{7}{4})& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}a-\frac{1}{4}x+\frac{1}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}a-\frac{1}{4}x+\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-\frac{13}{5})(\frac{18}{11}+p)& =(\color{red}{q}+\color{orange}{\frac{-13}{5}}).(\color{green}{p}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{11}q-\frac{13}{5}p-\frac{13}{5}.\frac{18}{11}& \text{Uitwerken } \\ & =pq+\frac{18}{11}q-\frac{13}{5}p-\frac{234}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-9}{8}+p)(\frac{10}{16}-b)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{-b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{8}p+\frac{9}{8}b-\frac{9}{8}.\frac{5}{8}& \text{Uitwerken } \\ & =-bp+\frac{5}{8}p+\frac{9}{8}b-\frac{45}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{18}+a)(a-\frac{15}{12})& =(\color{red}{a}+\color{orange}{\frac{-17}{18}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{4}a-\frac{17}{18}a+\frac{17}{18}.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{4})+(\frac{-17}{18}))a+\frac{85}{72} & \text{Neem samen} \\ &=a^2-\frac{79}{36}a+\frac{85}{72} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(b-\frac{-13}{11})(b+\frac{-2}{5})& =(\color{red}{b}+\color{orange}{\frac{13}{11}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{13}{11})} . \color{green}{(b)} + \color{orange}{(\frac{13}{11})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{5}b+\frac{13}{11}b-\frac{13}{11}.\frac{2}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{5})+\frac{13}{11})b-(\frac{-26}{55}) & \text{Neem samen} \\ &=b^2+\frac{43}{55}b-(\frac{-26}{55}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{18}{6}-a)(x+\frac{-6}{14})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{7}a+3x-3.\frac{3}{7}& \text{Uitwerken } \\ & =-ax+\frac{3}{7}a+3x-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{4}{6}+p)(b-\frac{13}{7})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{7}p+\frac{2}{3}b-\frac{2}{3}.\frac{13}{7}& \text{Uitwerken } \\ & =bp-\frac{13}{7}p+\frac{2}{3}b-\frac{26}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-3}{8}+p)(\frac{-12}{15}-q)& =(\color{red}{p}+\color{orange}{\frac{-3}{8}}).(\color{green}{-q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{5}p+\frac{3}{8}q+\frac{3}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =-pq-\frac{4}{5}p+\frac{3}{8}q+\frac{12}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{4}{5}p+\frac{3}{8}q+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)