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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-2}{12}+p)(\frac{9}{17}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{17}p+\frac{1}{6}a-\frac{1}{6}.\frac{9}{17}& \text{Uitwerken } \\ & =-ap+\frac{9}{17}p+\frac{1}{6}a-\frac{9}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{9}{17}p+\frac{1}{6}a-\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{14}{18})(\frac{-19}{6}-x)& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{-x}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{6}p+\frac{7}{9}x+\frac{7}{9}.\frac{19}{6}& \text{Uitwerken } \\ & =-px-\frac{19}{6}p+\frac{7}{9}x+\frac{133}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-18}{4})(p-\frac{15}{5})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3q+\frac{9}{2}p-\frac{9}{2}.3& \text{Uitwerken } \\ & =pq-3q+\frac{9}{2}p-\frac{27}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-9}{12})(\frac{11}{18}-p)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-p}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{18}q-\frac{3}{4}p+\frac{3}{4}.\frac{11}{18}& \text{Uitwerken } \\ & =-pq+\frac{11}{18}q-\frac{3}{4}p+\frac{33}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{11}{18}q-\frac{3}{4}p+\frac{11}{24} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-5}{8}-x)(\frac{14}{14}+a)& =(\color{red}{-x}+\color{orange}{\frac{-5}{8}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1x-\frac{5}{8}a-\frac{5}{8}.1& \text{Uitwerken } \\ & =-ax-1x-\frac{5}{8}a-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-16}{19}-b)(x+\frac{-2}{2})& =(\color{red}{-b}+\color{orange}{\frac{-16}{19}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1b-\frac{16}{19}x+\frac{16}{19}.1& \text{Uitwerken } \\ & =-bx+1b-\frac{16}{19}x+\frac{16}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{-7}{11})(q-\frac{4}{2})& =(\color{red}{p}+\color{orange}{\frac{-7}{11}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p-\frac{7}{11}q+\frac{7}{11}.2& \text{Uitwerken } \\ & =pq-2p-\frac{7}{11}q+\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{10}{5})(a+\frac{3}{12})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}x+2a+2.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}x+2a+\frac{2}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{4}x+2a+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b+\frac{15}{16})(p+\frac{15}{18})& =(\color{red}{b}+\color{orange}{\frac{15}{16}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{15}{16})} . \color{green}{(p)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{6}b+\frac{15}{16}p+\frac{15}{16}.\frac{5}{6}& \text{Uitwerken } \\ & =bp+\frac{5}{6}b+\frac{15}{16}p+\frac{75}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{6}b+\frac{15}{16}p+\frac{25}{32} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-2}{20}+p)(p-\frac{-7}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{15}p-\frac{1}{10}p-\frac{1}{10}.\frac{7}{15}& \text{Uitwerken } \\ & =p^2+(\frac{7}{15}+(\frac{-1}{10}))p-(\frac{-7}{150}) & \text{Neem samen} \\ &=p^2+\frac{11}{30}p-(\frac{-7}{150}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-5}{11}+x)(\frac{17}{3}-b)& =(\color{red}{x}+\color{orange}{\frac{-5}{11}}).(\color{green}{-b}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{3}x+\frac{5}{11}b-\frac{5}{11}.\frac{17}{3}& \text{Uitwerken } \\ & =-bx+\frac{17}{3}x+\frac{5}{11}b-\frac{85}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{20}{5})(q-\frac{5}{14})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{14}x-4q+4.\frac{5}{14}& \text{Uitwerken } \\ & =qx-\frac{5}{14}x-4q+\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{14}x-4q+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)