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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{8}{12})(\frac{14}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{6}p-\frac{2}{3}b-\frac{2}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =bp+\frac{7}{6}p-\frac{2}{3}b-\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{6}p-\frac{2}{3}b-\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-11}{6}-q)(\frac{18}{6}+p)& =(\color{red}{-q}+\color{orange}{\frac{-11}{6}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(3)} + \color{orange}{(\frac{-11}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -pq-3q-\frac{11}{6}p-\frac{11}{6}.3& \text{Uitwerken } \\ & =-pq-3q-\frac{11}{6}p-\frac{33}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-3q-\frac{11}{6}p-\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{-7}{17})(\frac{11}{6}+q)& =(\color{red}{b}+\color{orange}{\frac{7}{17}}).(\color{green}{q}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{6}b+\frac{7}{17}q+\frac{7}{17}.\frac{11}{6}& \text{Uitwerken } \\ & =bq+\frac{11}{6}b+\frac{7}{17}q+\frac{77}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-16}{6}-q)(b-\frac{3}{15})& =(\color{red}{-q}+\color{orange}{\frac{-8}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{5}q-\frac{8}{3}b+\frac{8}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =-bq+\frac{1}{5}q-\frac{8}{3}b+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{2}{6}+x)(\frac{-12}{5}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{5}x+\frac{1}{3}b-\frac{1}{3}.\frac{12}{5}& \text{Uitwerken } \\ & =bx-\frac{12}{5}x+\frac{1}{3}b-\frac{12}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{12}{5}x+\frac{1}{3}b-\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a-15)(\frac{2}{6}+x)& =(\color{red}{a}+\color{orange}{(-15)}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-15)} . \color{green}{(x)} + \color{orange}{(-15)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{3}a-15x-15.\frac{1}{3}& \text{Uitwerken } \\ & =ax+\frac{1}{3}a-15x-\frac{15}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{3}a-15x-5 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{11}{7})(\frac{18}{11}-p)& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{-p}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{11}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{18}{11}q-\frac{11}{7}p+\frac{11}{7}.\frac{18}{11}& \text{Uitwerken } \\ & =-pq+\frac{18}{11}q-\frac{11}{7}p+\frac{198}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{18}{11}q-\frac{11}{7}p+\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q-\frac{20}{13})(a+\frac{17}{17})& =(\color{red}{q}+\color{orange}{\frac{-20}{13}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-20}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1q-\frac{20}{13}a-\frac{20}{13}.1& \text{Uitwerken } \\ & =aq+1q-\frac{20}{13}a-\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{2}{12})(q+\frac{13}{17})& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{q}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{1}{6})} . \color{green}{(q)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{17}b+\frac{1}{6}q+\frac{1}{6}.\frac{13}{17}& \text{Uitwerken } \\ & =bq+\frac{13}{17}b+\frac{1}{6}q+\frac{13}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{15}{18}+p)(\frac{-17}{4}-p)& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{-p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{4}p-\frac{5}{6}p-\frac{5}{6}.\frac{17}{4}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{4})+(\frac{-5}{6}))p-\frac{85}{24} & \text{Neem samen} \\ &=-p^2-\frac{61}{12}p-\frac{85}{24} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{17}+q)(a-\frac{-17}{13})& =(\color{red}{q}+\color{orange}{\frac{-8}{17}}).(\color{green}{a}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{13}q-\frac{8}{17}a-\frac{8}{17}.\frac{17}{13}& \text{Uitwerken } \\ & =aq+\frac{17}{13}q-\frac{8}{17}a-\frac{136}{221} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{17}{13}q-\frac{8}{17}a-\frac{8}{13} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a+\frac{-5}{15})(x+\frac{-10}{15})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{3}a-\frac{1}{3}x+\frac{1}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =ax-\frac{2}{3}a-\frac{1}{3}x+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)