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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{3}{17})(\frac{10}{6}-x)& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{-x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{3}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{3}a-\frac{3}{17}x+\frac{3}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =-ax+\frac{5}{3}a-\frac{3}{17}x+\frac{15}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{3}a-\frac{3}{17}x+\frac{5}{17} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{6}{18}+a)(\frac{-19}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{17}a+\frac{1}{3}q-\frac{1}{3}.\frac{19}{17}& \text{Uitwerken } \\ & =aq-\frac{19}{17}a+\frac{1}{3}q-\frac{19}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{-9}{14})(a+\frac{15}{2})& =(\color{red}{p}+\color{orange}{\frac{9}{14}}).(\color{green}{a}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{15}{2}p+\frac{9}{14}a+\frac{9}{14}.\frac{15}{2}& \text{Uitwerken } \\ & =ap+\frac{15}{2}p+\frac{9}{14}a+\frac{135}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{7}+p)(x-\frac{-5}{7})& =(\color{red}{p}+\color{orange}{\frac{16}{7}}).(\color{green}{x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{16}{7})} . \color{green}{(x)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{7}p+\frac{16}{7}x+\frac{16}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =px+\frac{5}{7}p+\frac{16}{7}x+\frac{80}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{11}{8})(b-\frac{8}{12})& =(\color{red}{b}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{3}b+\frac{11}{8}b-\frac{11}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{3})+\frac{11}{8})b-(\frac{-22}{24}) & \text{Neem samen} \\ &=b^2+\frac{17}{24}b-(\frac{-22}{24}) & \text{Maak de som} \\ &=b^2+\frac{17}{24}b+\frac{11}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{9}+p)((-15)-q)& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{-q}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-15)} + \color{orange}{(\frac{-7}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = -pq-15p+\frac{7}{9}q+\frac{7}{9}.15& \text{Uitwerken } \\ & =-pq-15p+\frac{7}{9}q+\frac{105}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-15p+\frac{7}{9}q+\frac{35}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-12}{11}-a)(p-\frac{-12}{6})& =(\color{red}{-a}+\color{orange}{\frac{-12}{11}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{-12}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap-2a-\frac{12}{11}p-\frac{12}{11}.2& \text{Uitwerken } \\ & =-ap-2a-\frac{12}{11}p-\frac{24}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{10}{15}+q)(b+\frac{3}{4})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{4}q+\frac{2}{3}b+\frac{2}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =bq+\frac{3}{4}q+\frac{2}{3}b+\frac{6}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{3}{4}q+\frac{2}{3}b+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-16}{8}+a)(p-\frac{3}{5})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{5}a-2p+2.\frac{3}{5}& \text{Uitwerken } \\ & =ap-\frac{3}{5}a-2p+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{12}-a)(x-\frac{14}{5})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{14}{5}a+\frac{3}{2}x-\frac{3}{2}.\frac{14}{5}& \text{Uitwerken } \\ & =-ax+\frac{14}{5}a+\frac{3}{2}x-\frac{42}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{14}{5}a+\frac{3}{2}x-\frac{21}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{8}{15}-b)(a+\frac{8}{18})& =(\color{red}{-b}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{9}b+\frac{8}{15}a+\frac{8}{15}.\frac{4}{9}& \text{Uitwerken } \\ & =-ab-\frac{4}{9}b+\frac{8}{15}a+\frac{32}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{10}{18})(p+\frac{12}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{9}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4q+\frac{5}{9}p+\frac{5}{9}.4& \text{Uitwerken } \\ & =pq+4q+\frac{5}{9}p+\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)