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

Hoofdmenu Eentje per keer  🖨

Werk uit en vereenvoudig

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

---

Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{7}{2}+p)(\frac{6}{11}+a)& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{7}{2})} . \color{green}{(a)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{11}p+\frac{7}{2}a+\frac{7}{2}.\frac{6}{11}& \text{Uitwerken } \\ & =ap+\frac{6}{11}p+\frac{7}{2}a+\frac{42}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{11}p+\frac{7}{2}a+\frac{21}{11} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{14}-p)(\frac{-10}{14}-p)& =(\color{red}{-p}+\color{orange}{\frac{-9}{7}}).(\color{green}{-p}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{7}p+\frac{9}{7}p+\frac{9}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =p^2+(\frac{5}{7}+\frac{9}{7})p+\frac{45}{49} & \text{Neem samen} \\ &=p^2+\frac{14}{7}p+\frac{45}{49} & \text{Maak de som} \\ &=p^2+2p+\frac{45}{49} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{17}{10}-q)(p+\frac{-9}{4})& =(\color{red}{-q}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{4}q+\frac{17}{10}p-\frac{17}{10}.\frac{9}{4}& \text{Uitwerken } \\ & =-pq+\frac{9}{4}q+\frac{17}{10}p-\frac{153}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{20}{7})(b+\frac{18}{3})& =(\color{red}{q}+\color{orange}{\frac{-20}{7}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-20}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bq+6q-\frac{20}{7}b-\frac{20}{7}.6& \text{Uitwerken } \\ & =bq+6q-\frac{20}{7}b-\frac{120}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{-18}{13})(x+\frac{-2}{14})& =(\color{red}{b}+\color{orange}{\frac{-18}{13}}).(\color{green}{x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{7}b-\frac{18}{13}x+\frac{18}{13}.\frac{1}{7}& \text{Uitwerken } \\ & =bx-\frac{1}{7}b-\frac{18}{13}x+\frac{18}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{11}{9})(x-\frac{3}{8})& =(\color{red}{a}+\color{orange}{\frac{11}{9}}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{8}a+\frac{11}{9}x-\frac{11}{9}.\frac{3}{8}& \text{Uitwerken } \\ & =ax-\frac{3}{8}a+\frac{11}{9}x-\frac{33}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{8}a+\frac{11}{9}x-\frac{11}{24} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{5}+p)(\frac{8}{16}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{-a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}p+\frac{1}{5}a-\frac{1}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}p+\frac{1}{5}a-\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{-17}{10})(\frac{-3}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{6}b+\frac{17}{10}p-\frac{17}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =bp-\frac{1}{6}b+\frac{17}{10}p-\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-7}{4})(a-\frac{-20}{14})& =(\color{red}{b}+\color{orange}{\frac{-7}{4}}).(\color{green}{a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{7}b-\frac{7}{4}a-\frac{7}{4}.\frac{10}{7}& \text{Uitwerken } \\ & =ab+\frac{10}{7}b-\frac{7}{4}a-\frac{70}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{10}{7}b-\frac{7}{4}a-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{-8}{10})(\frac{7}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{7}{20}p-\frac{4}{5}p-\frac{4}{5}.\frac{7}{20}& \text{Uitwerken } \\ & =p^2+(\frac{7}{20}+(\frac{-4}{5}))p-(\frac{-28}{100}) & \text{Neem samen} \\ &=p^2-\frac{9}{20}p-(\frac{-28}{100}) & \text{Maak de som} \\ &=p^2-\frac{9}{20}p+\frac{7}{25} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
11. \(\begin{align}(\frac{11}{20}+a)(x-\frac{-9}{19})& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{11}{20})} . \color{green}{(x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{19}a+\frac{11}{20}x+\frac{11}{20}.\frac{9}{19}& \text{Uitwerken } \\ & =ax+\frac{9}{19}a+\frac{11}{20}x+\frac{99}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-12}{14}-b)(b+\frac{-17}{5})& =(\color{red}{-b}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{5}b-\frac{6}{7}b+\frac{6}{7}.\frac{17}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{5}+(\frac{-6}{7}))b+(\frac{-102}{35}) & \text{Neem samen} \\ &=-b^2+\frac{89}{35}b+(\frac{-102}{35}) & \text{Maak de som} \\\end{align}\)