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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{2}{3}-b)(a-\frac{-9}{11})& =(\color{red}{-b}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{11}b+\frac{2}{3}a+\frac{2}{3}.\frac{9}{11}& \text{Uitwerken } \\ & =-ab-\frac{9}{11}b+\frac{2}{3}a+\frac{18}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{9}{11}b+\frac{2}{3}a+\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a+\frac{9}{3})(\frac{-3}{14}+a)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{14}a+3a-3.\frac{3}{14}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{14})+3)a-(\frac{-9}{14}) & \text{Neem samen} \\ &=a^2+\frac{39}{14}a-(\frac{-9}{14}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{11}{2}-a)(\frac{6}{3}+a)& =(\color{red}{-a}+\color{orange}{\frac{11}{2}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aa-2a+\frac{11}{2}a+\frac{11}{2}.2& \text{Uitwerken } \\ & =-a^2+((-2)+\frac{11}{2})a+(\frac{-22}{2}) & \text{Neem samen} \\ &=-a^2+\frac{7}{2}a+(\frac{-22}{2}) & \text{Maak de som} \\ &=-a^2+\frac{7}{2}a+(-11) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(p-\frac{6}{14})(q-\frac{-18}{12})& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{2}p-\frac{3}{7}q-\frac{3}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =pq+\frac{3}{2}p-\frac{3}{7}q-\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{8}{14})(a-\frac{-17}{12})& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{12}p+\frac{4}{7}a+\frac{4}{7}.\frac{17}{12}& \text{Uitwerken } \\ & =ap+\frac{17}{12}p+\frac{4}{7}a+\frac{68}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{17}{12}p+\frac{4}{7}a+\frac{17}{21} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-5}{19}+b)(\frac{-20}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{19}}).(\color{green}{-a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{20}{7}b+\frac{5}{19}a+\frac{5}{19}.\frac{20}{7}& \text{Uitwerken } \\ & =-ab-\frac{20}{7}b+\frac{5}{19}a+\frac{100}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{16}+q)(\frac{1}{10}+b)& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{7}{16})} . \color{green}{(b)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{10}q+\frac{7}{16}b+\frac{7}{16}.\frac{1}{10}& \text{Uitwerken } \\ & =bq+\frac{1}{10}q+\frac{7}{16}b+\frac{7}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-13}{8}+p)(\frac{12}{4}+p)& =(\color{red}{p}+\color{orange}{\frac{-13}{8}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-13}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pp+3p-\frac{13}{8}p-\frac{13}{8}.3& \text{Uitwerken } \\ & =p^2+(3+(\frac{-13}{8}))p-(\frac{-39}{8}) & \text{Neem samen} \\ &=p^2+\frac{11}{8}p-(\frac{-39}{8}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(x-\frac{8}{5})(\frac{10}{5}+x)& =(\color{red}{x}+\color{orange}{\frac{-8}{5}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-8}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x-\frac{8}{5}x-\frac{8}{5}.2& \text{Uitwerken } \\ & =x^2+(2+(\frac{-8}{5}))x-(\frac{-16}{5}) & \text{Neem samen} \\ &=x^2+\frac{2}{5}x-(\frac{-16}{5}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{-9}{20})(\frac{-19}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{-9}{20}}).(\color{green}{p}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{2}a-\frac{9}{20}p+\frac{9}{20}.\frac{19}{2}& \text{Uitwerken } \\ & =ap-\frac{19}{2}a-\frac{9}{20}p+\frac{171}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-14}{10}+p)(p+\frac{17}{12})& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{12}p-\frac{7}{5}p-\frac{7}{5}.\frac{17}{12}& \text{Uitwerken } \\ & =p^2+(\frac{17}{12}+(\frac{-7}{5}))p-(\frac{-119}{60}) & \text{Neem samen} \\ &=p^2+\frac{1}{60}p-(\frac{-119}{60}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-12}{14}-a)(a+\frac{8}{10})& =(\color{red}{-a}+\color{orange}{\frac{-6}{7}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{4}{5}a-\frac{6}{7}a-\frac{6}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-4}{5})+(\frac{-6}{7}))a-\frac{24}{35} & \text{Neem samen} \\ &=-a^2-\frac{58}{35}a-\frac{24}{35} & \text{Maak de som} \\\end{align}\)