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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{4}{3}-a)(a-\frac{16}{17})& =(\color{red}{-a}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{16}{17}a+\frac{4}{3}a-\frac{4}{3}.\frac{16}{17}& \text{Uitwerken } \\ & =-a^2+(\frac{16}{17}+\frac{4}{3})a-\frac{64}{51} & \text{Neem samen} \\ &=-a^2+\frac{116}{51}a-\frac{64}{51} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(q+\frac{-17}{20})(q+\frac{-12}{12})& =(\color{red}{q}+\color{orange}{\frac{-17}{20}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q-\frac{17}{20}q+\frac{17}{20}.1& \text{Uitwerken } \\ & =q^2+((-1)+(\frac{-17}{20}))q+\frac{17}{20} & \text{Neem samen} \\ &=q^2-\frac{37}{20}q+\frac{17}{20} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(a+\frac{9}{11})(b+\frac{20}{17})& =(\color{red}{a}+\color{orange}{\frac{9}{11}}).(\color{green}{b}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{9}{11})} . \color{green}{(b)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{17}a+\frac{9}{11}b+\frac{9}{11}.\frac{20}{17}& \text{Uitwerken } \\ & =ab+\frac{20}{17}a+\frac{9}{11}b+\frac{180}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{-2}{16})(\frac{18}{11}-a)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{-a}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{18}{11}a-\frac{1}{8}a+\frac{1}{8}.\frac{18}{11}& \text{Uitwerken } \\ & =-a^2+(\frac{18}{11}+(\frac{-1}{8}))a+(\frac{-18}{88}) & \text{Neem samen} \\ &=-a^2+\frac{133}{88}a+(\frac{-18}{88}) & \text{Maak de som} \\ &=-a^2+\frac{133}{88}a+(\frac{-9}{44}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(a-\frac{-17}{11})(\frac{-16}{15}+x)& =(\color{red}{a}+\color{orange}{\frac{17}{11}}).(\color{green}{x}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{15}a+\frac{17}{11}x-\frac{17}{11}.\frac{16}{15}& \text{Uitwerken } \\ & =ax-\frac{16}{15}a+\frac{17}{11}x-\frac{272}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{16}{16})(\frac{-8}{7}+a)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{7}p-1a+1.\frac{8}{7}& \text{Uitwerken } \\ & =ap-\frac{8}{7}p-1a+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-9}{13}-p)(\frac{-12}{13}-b)& =(\color{red}{-p}+\color{orange}{\frac{-9}{13}}).(\color{green}{-b}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{13}p+\frac{9}{13}b+\frac{9}{13}.\frac{12}{13}& \text{Uitwerken } \\ & =bp+\frac{12}{13}p+\frac{9}{13}b+\frac{108}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{17}-a)(a+\frac{3}{9})& =(\color{red}{-a}+\color{orange}{\frac{3}{17}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{3}{17})} . \color{green}{(a)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{3}a+\frac{3}{17}a+\frac{3}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{3})+\frac{3}{17})a+(\frac{-3}{51}) & \text{Neem samen} \\ &=-a^2-\frac{8}{51}a+(\frac{-3}{51}) & \text{Maak de som} \\ &=-a^2-\frac{8}{51}a+(\frac{-1}{17}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{7}{11}-p)(a+\frac{-6}{9})& =(\color{red}{-p}+\color{orange}{\frac{7}{11}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{7}{11})} . \color{green}{(a)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{3}p+\frac{7}{11}a-\frac{7}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap+\frac{2}{3}p+\frac{7}{11}a-\frac{14}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-13}{18}-b)(\frac{-5}{16}+p)& =(\color{red}{-b}+\color{orange}{\frac{-13}{18}}).(\color{green}{p}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{16}b-\frac{13}{18}p+\frac{13}{18}.\frac{5}{16}& \text{Uitwerken } \\ & =-bp+\frac{5}{16}b-\frac{13}{18}p+\frac{65}{288} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{17}{19})(p-\frac{13}{10})& =(\color{red}{a}+\color{orange}{\frac{17}{19}}).(\color{green}{p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{10}a+\frac{17}{19}p-\frac{17}{19}.\frac{13}{10}& \text{Uitwerken } \\ & =ap-\frac{13}{10}a+\frac{17}{19}p-\frac{221}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(16-a)(x+\frac{6}{18})& =(\color{red}{-a}+\color{orange}{16}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(16)} . \color{green}{(x)} + \color{orange}{(16)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{3}a+16x+16.\frac{1}{3}& \text{Uitwerken } \\ & =-ax-\frac{1}{3}a+16x+\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)