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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{9}{18}-b)(b+\frac{-16}{17})& =(\color{red}{-b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{16}{17}b+\frac{1}{2}b-\frac{1}{2}.\frac{16}{17}& \text{Uitwerken } \\ & =-b^2+(\frac{16}{17}+\frac{1}{2})b-\frac{16}{34} & \text{Neem samen} \\ &=-b^2+\frac{49}{34}b-\frac{16}{34} & \text{Maak de som} \\ &=-b^2+\frac{49}{34}b-\frac{8}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(\frac{-13}{13}+p)(\frac{13}{4}-x)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{4}p+1x-1.\frac{13}{4}& \text{Uitwerken } \\ & =-px+\frac{13}{4}p+1x-\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{14}{11}-b)(\frac{-16}{18}+b)& =(\color{red}{-b}+\color{orange}{\frac{14}{11}}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{8}{9}b+\frac{14}{11}b-\frac{14}{11}.\frac{8}{9}& \text{Uitwerken } \\ & =-b^2+(\frac{8}{9}+\frac{14}{11})b-\frac{112}{99} & \text{Neem samen} \\ &=-b^2+\frac{214}{99}b-\frac{112}{99} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b-\frac{7}{19})(b-\frac{-19}{13})& =(\color{red}{b}+\color{orange}{\frac{-7}{19}}).(\color{green}{b}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{19}{13}b-\frac{7}{19}b-\frac{7}{19}.\frac{19}{13}& \text{Uitwerken } \\ & =b^2+(\frac{19}{13}+(\frac{-7}{19}))b-(\frac{-133}{247}) & \text{Neem samen} \\ &=b^2+\frac{270}{247}b-(\frac{-133}{247}) & \text{Maak de som} \\ &=b^2+\frac{270}{247}b+\frac{7}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(b-\frac{-16}{3})((-16)+p)& =(\color{red}{b}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-16)} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = bp-16b+\frac{16}{3}p-\frac{16}{3}.16& \text{Uitwerken } \\ & =bp-16b+\frac{16}{3}p-\frac{256}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{14}{19})(q+\frac{13}{12})& =(\color{red}{q}+\color{orange}{\frac{14}{19}}).(\color{green}{q}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{13}{12}q+\frac{14}{19}q+\frac{14}{19}.\frac{13}{12}& \text{Uitwerken } \\ & =q^2+(\frac{13}{12}+\frac{14}{19})q+\frac{182}{228} & \text{Neem samen} \\ &=q^2+\frac{415}{228}q+\frac{182}{228} & \text{Maak de som} \\ &=q^2+\frac{415}{228}q+\frac{91}{114} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{13}-x)(x+\frac{-3}{3})& =(\color{red}{-x}+\color{orange}{\frac{-11}{13}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -xx+1x-\frac{11}{13}x+\frac{11}{13}.1& \text{Uitwerken } \\ & =-x^2+(1+(\frac{-11}{13}))x+(\frac{-11}{13}) & \text{Neem samen} \\ &=-x^2+\frac{2}{13}x+(\frac{-11}{13}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a-\frac{2}{13})(\frac{-1}{3}-x)& =(\color{red}{a}+\color{orange}{\frac{-2}{13}}).(\color{green}{-x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{3}a+\frac{2}{13}x+\frac{2}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =-ax-\frac{1}{3}a+\frac{2}{13}x+\frac{2}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{7}+q)(x+\frac{13}{12})& =(\color{red}{q}+\color{orange}{\frac{-3}{7}}).(\color{green}{x}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{12}q-\frac{3}{7}x-\frac{3}{7}.\frac{13}{12}& \text{Uitwerken } \\ & =qx+\frac{13}{12}q-\frac{3}{7}x-\frac{39}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{12}q-\frac{3}{7}x-\frac{13}{28} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{17}{15}+x)(b+\frac{10}{8})& =(\color{red}{x}+\color{orange}{\frac{17}{15}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{17}{15})} . \color{green}{(b)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{4}x+\frac{17}{15}b+\frac{17}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =bx+\frac{5}{4}x+\frac{17}{15}b+\frac{85}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{4}x+\frac{17}{15}b+\frac{17}{12} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{14}+a)(a+\frac{12}{2})& =(\color{red}{a}+\color{orange}{\frac{-4}{7}}).(\color{green}{a}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = aa+6a-\frac{4}{7}a-\frac{4}{7}.6& \text{Uitwerken } \\ & =a^2+(6+(\frac{-4}{7}))a-(\frac{-24}{7}) & \text{Neem samen} \\ &=a^2+\frac{38}{7}a-(\frac{-24}{7}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(x-\frac{17}{4})(\frac{18}{20}-b)& =(\color{red}{x}+\color{orange}{\frac{-17}{4}}).(\color{green}{-b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{10}x+\frac{17}{4}b-\frac{17}{4}.\frac{9}{10}& \text{Uitwerken } \\ & =-bx+\frac{9}{10}x+\frac{17}{4}b-\frac{153}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)