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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-9}{10}-p)(b-\frac{-16}{19})& =(\color{red}{-p}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{19}p-\frac{9}{10}b-\frac{9}{10}.\frac{16}{19}& \text{Uitwerken } \\ & =-bp-\frac{16}{19}p-\frac{9}{10}b-\frac{144}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{16}{19}p-\frac{9}{10}b-\frac{72}{95} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{11}+a)(\frac{-7}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{-9}{11}}).(\color{green}{a}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{19}a-\frac{9}{11}a+\frac{9}{11}.\frac{7}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{19})+(\frac{-9}{11}))a+\frac{63}{209} & \text{Neem samen} \\ &=a^2-\frac{248}{209}a+\frac{63}{209} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{11}+b)(\frac{19}{2}-a)& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{-a}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{2}b+\frac{19}{11}a-\frac{19}{11}.\frac{19}{2}& \text{Uitwerken } \\ & =-ab+\frac{19}{2}b+\frac{19}{11}a-\frac{361}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{14}{12})(\frac{-3}{4}-a)& =(\color{red}{p}+\color{orange}{\frac{7}{6}}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{4}p-\frac{7}{6}a-\frac{7}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-ap-\frac{3}{4}p-\frac{7}{6}a-\frac{21}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{4}p-\frac{7}{6}a-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{1}{20}-b)((-8)+p)& =(\color{red}{-b}+\color{orange}{\frac{1}{20}}).(\color{green}{p}+\color{blue}{(-8)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{20})} . \color{green}{(p)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -bp+8b+\frac{1}{20}p-\frac{1}{20}.8& \text{Uitwerken } \\ & =-bp+8b+\frac{1}{20}p-\frac{8}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+8b+\frac{1}{20}p-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{-17}{19})(q+\frac{-16}{4})& =(\color{red}{x}+\color{orange}{\frac{17}{19}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{17}{19})} . \color{green}{(q)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4x+\frac{17}{19}q-\frac{17}{19}.4& \text{Uitwerken } \\ & =qx-4x+\frac{17}{19}q-\frac{68}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{19}+q)(a+\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{-4}{19}}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{9}q-\frac{4}{19}a+\frac{4}{19}.\frac{4}{9}& \text{Uitwerken } \\ & =aq-\frac{4}{9}q-\frac{4}{19}a+\frac{16}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{16}{20}+q)(a-\frac{-16}{9})& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{9}q+\frac{4}{5}a+\frac{4}{5}.\frac{16}{9}& \text{Uitwerken } \\ & =aq+\frac{16}{9}q+\frac{4}{5}a+\frac{64}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{19}{4}+p)(q-\frac{17}{20})& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{q}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{20}p+\frac{19}{4}q-\frac{19}{4}.\frac{17}{20}& \text{Uitwerken } \\ & =pq-\frac{17}{20}p+\frac{19}{4}q-\frac{323}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{3}{10}-b)(\frac{5}{17}+x)& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{17}b+\frac{3}{10}x+\frac{3}{10}.\frac{5}{17}& \text{Uitwerken } \\ & =-bx-\frac{5}{17}b+\frac{3}{10}x+\frac{15}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{17}b+\frac{3}{10}x+\frac{3}{34} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{-10}{19})(10-q)& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{-q}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(10)} + \color{orange}{(\frac{10}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -qx+10x-\frac{10}{19}q+\frac{10}{19}.10& \text{Uitwerken } \\ & =-qx+10x-\frac{10}{19}q+\frac{100}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{20}{16}-a)(x-\frac{5}{12})& =(\color{red}{-a}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{12}a+\frac{5}{4}x-\frac{5}{4}.\frac{5}{12}& \text{Uitwerken } \\ & =-ax+\frac{5}{12}a+\frac{5}{4}x-\frac{25}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)