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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-17}{20}-a)(a-\frac{-7}{3})& =(\color{red}{-a}+\color{orange}{\frac{-17}{20}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{7}{3}a-\frac{17}{20}a-\frac{17}{20}.\frac{7}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-7}{3})+(\frac{-17}{20}))a-\frac{119}{60} & \text{Neem samen} \\ &=-a^2-\frac{191}{60}a-\frac{119}{60} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(a+\frac{12}{12})(q+\frac{5}{17})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{17}a+1q+1.\frac{5}{17}& \text{Uitwerken } \\ & =aq+\frac{5}{17}a+1q+\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-14}{16}-x)(\frac{-18}{4}+a)& =(\color{red}{-x}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{2}x-\frac{7}{8}a+\frac{7}{8}.\frac{9}{2}& \text{Uitwerken } \\ & =-ax+\frac{9}{2}x-\frac{7}{8}a+\frac{63}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{19}{13}+x)(b-\frac{-10}{3})& =(\color{red}{x}+\color{orange}{\frac{19}{13}}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{19}{13})} . \color{green}{(b)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{3}x+\frac{19}{13}b+\frac{19}{13}.\frac{10}{3}& \text{Uitwerken } \\ & =bx+\frac{10}{3}x+\frac{19}{13}b+\frac{190}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-2}{8})(\frac{15}{10}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{2}a+\frac{1}{4}p+\frac{1}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =ap+\frac{3}{2}a+\frac{1}{4}p+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{18}{12}+a)(a+\frac{-8}{13})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{8}{13}a+\frac{3}{2}a-\frac{3}{2}.\frac{8}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-8}{13})+\frac{3}{2})a-(\frac{-24}{26}) & \text{Neem samen} \\ &=a^2+\frac{23}{26}a-(\frac{-24}{26}) & \text{Maak de som} \\ &=a^2+\frac{23}{26}a+\frac{12}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(\frac{2}{13}+b)(q-\frac{-19}{13})& =(\color{red}{b}+\color{orange}{\frac{2}{13}}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{2}{13})} . \color{green}{(q)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{13}b+\frac{2}{13}q+\frac{2}{13}.\frac{19}{13}& \text{Uitwerken } \\ & =bq+\frac{19}{13}b+\frac{2}{13}q+\frac{38}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{1}{17})(b+\frac{-4}{13})& =(\color{red}{x}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{13}x-\frac{1}{17}b+\frac{1}{17}.\frac{4}{13}& \text{Uitwerken } \\ & =bx-\frac{4}{13}x-\frac{1}{17}b+\frac{4}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{-14}{10})(\frac{-17}{11}+q)& =(\color{red}{a}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{11}a-\frac{7}{5}q+\frac{7}{5}.\frac{17}{11}& \text{Uitwerken } \\ & =aq-\frac{17}{11}a-\frac{7}{5}q+\frac{119}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-1}{6})(x+(-3))& =(\color{red}{a}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3a-\frac{1}{6}x+\frac{1}{6}.3& \text{Uitwerken } \\ & =ax-3a-\frac{1}{6}x+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-3a-\frac{1}{6}x+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{14}-q)(p-\frac{-1}{4})& =(\color{red}{-q}+\color{orange}{\frac{-9}{14}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{4}q-\frac{9}{14}p-\frac{9}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =-pq-\frac{1}{4}q-\frac{9}{14}p-\frac{9}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{18}{18}-b)(p-\frac{2}{6})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{3}b+1p-1.\frac{1}{3}& \text{Uitwerken } \\ & =-bp+\frac{1}{3}b+1p-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)