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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{10}{4}+a)(\frac{-1}{19}-b)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{-b}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{19}a-\frac{5}{2}b-\frac{5}{2}.\frac{1}{19}& \text{Uitwerken } \\ & =-ab-\frac{1}{19}a-\frac{5}{2}b-\frac{5}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{3}{15}+a)(\frac{-2}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{8}a+\frac{1}{5}b-\frac{1}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =ab-\frac{1}{8}a+\frac{1}{5}b-\frac{1}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{1}{18})(q-\frac{11}{2})& =(\color{red}{q}+\color{orange}{\frac{1}{18}}).(\color{green}{q}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{1}{18})} . \color{green}{(q)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{2}q+\frac{1}{18}q-\frac{1}{18}.\frac{11}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{2})+\frac{1}{18})q-(\frac{-11}{36}) & \text{Neem samen} \\ &=q^2-\frac{98}{18}q-(\frac{-11}{36}) & \text{Maak de som} \\ &=q^2-\frac{49}{9}q+\frac{11}{36} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(a-\frac{9}{14})(q+9)& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{q}+\color{blue}{9})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(9)} + \color{orange}{(\frac{-9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = aq+9a-\frac{9}{14}q-\frac{9}{14}.9& \text{Uitwerken } \\ & =aq+9a-\frac{9}{14}q-\frac{81}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{16}{8}-p)(q-\frac{-13}{18})& =(\color{red}{-p}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{18}p+2q+2.\frac{13}{18}& \text{Uitwerken } \\ & =-pq-\frac{13}{18}p+2q+\frac{26}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{13}{18}p+2q+\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{20}{7}+a)(p-\frac{14}{13})& =(\color{red}{a}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{13}a+\frac{20}{7}p-\frac{20}{7}.\frac{14}{13}& \text{Uitwerken } \\ & =ap-\frac{14}{13}a+\frac{20}{7}p-\frac{280}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{14}{13}a+\frac{20}{7}p-\frac{40}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{19}{14})(\frac{11}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{-19}{14}}).(\color{green}{p}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{9}b-\frac{19}{14}p-\frac{19}{14}.\frac{11}{9}& \text{Uitwerken } \\ & =bp+\frac{11}{9}b-\frac{19}{14}p-\frac{209}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-19}{13}-a)(\frac{-17}{15}-x)& =(\color{red}{-a}+\color{orange}{\frac{-19}{13}}).(\color{green}{-x}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{15}a+\frac{19}{13}x+\frac{19}{13}.\frac{17}{15}& \text{Uitwerken } \\ & =ax+\frac{17}{15}a+\frac{19}{13}x+\frac{323}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{16}{3}-b)(p+\frac{-1}{9})& =(\color{red}{-b}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{9}b+\frac{16}{3}p-\frac{16}{3}.\frac{1}{9}& \text{Uitwerken } \\ & =-bp+\frac{1}{9}b+\frac{16}{3}p-\frac{16}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{16}-x)(x-\frac{8}{10})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{5}x-1x+1.\frac{4}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{5}+(-1))x+(\frac{-4}{5}) & \text{Neem samen} \\ &=-x^2-\frac{1}{5}x+(\frac{-4}{5}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-12}{20}-b)(b+\frac{-10}{4})& =(\color{red}{-b}+\color{orange}{\frac{-3}{5}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{5}{2}b-\frac{3}{5}b+\frac{3}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{5}{2}+(\frac{-3}{5}))b+(\frac{-15}{10}) & \text{Neem samen} \\ &=-b^2+\frac{19}{10}b+(\frac{-15}{10}) & \text{Maak de som} \\ &=-b^2+\frac{19}{10}b+(\frac{-3}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(x-\frac{15}{10})(\frac{-19}{5}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{5}x+\frac{3}{2}q+\frac{3}{2}.\frac{19}{5}& \text{Uitwerken } \\ & =-qx-\frac{19}{5}x+\frac{3}{2}q+\frac{57}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)