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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{11}-q)((-15)-a)& =(\color{red}{-q}+\color{orange}{\frac{19}{11}}).(\color{green}{-a}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(-15)} + \color{orange}{(\frac{19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = aq+15q-\frac{19}{11}a-\frac{19}{11}.15& \text{Uitwerken } \\ & =aq+15q-\frac{19}{11}a-\frac{285}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{5}{20})(\frac{-8}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{5}p-\frac{1}{4}q+\frac{1}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =pq-\frac{2}{5}p-\frac{1}{4}q+\frac{2}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{5}p-\frac{1}{4}q+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{8}{15}+x)(\frac{-3}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{8}{15}}).(\color{green}{-b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{8}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{5}x-\frac{8}{15}b-\frac{8}{15}.\frac{1}{5}& \text{Uitwerken } \\ & =-bx-\frac{1}{5}x-\frac{8}{15}b-\frac{8}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{4}{9})(b-\frac{-15}{11})& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{b}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{11}q-\frac{4}{9}b-\frac{4}{9}.\frac{15}{11}& \text{Uitwerken } \\ & =bq+\frac{15}{11}q-\frac{4}{9}b-\frac{60}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{15}{11}q-\frac{4}{9}b-\frac{20}{33} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(a+\frac{-15}{12})(\frac{-16}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{p}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{9}a-\frac{5}{4}p+\frac{5}{4}.\frac{16}{9}& \text{Uitwerken } \\ & =ap-\frac{16}{9}a-\frac{5}{4}p+\frac{80}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{16}{9}a-\frac{5}{4}p+\frac{20}{9} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{14}{5}-b)(a+\frac{12}{15})& =(\color{red}{-b}+\color{orange}{\frac{14}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{14}{5})} . \color{green}{(a)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}b+\frac{14}{5}a+\frac{14}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}b+\frac{14}{5}a+\frac{56}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{10}{19})(a-\frac{17}{2})& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{2}x+\frac{10}{19}a-\frac{10}{19}.\frac{17}{2}& \text{Uitwerken } \\ & =ax-\frac{17}{2}x+\frac{10}{19}a-\frac{170}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{17}{2}x+\frac{10}{19}a-\frac{85}{19} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p-\frac{9}{9})(\frac{-2}{11}+b)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{11}p-1b+1.\frac{2}{11}& \text{Uitwerken } \\ & =bp-\frac{2}{11}p-1b+\frac{2}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{7}{14})(\frac{3}{3}-x)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1a+\frac{1}{2}x-\frac{1}{2}.1& \text{Uitwerken } \\ & =-ax+1a+\frac{1}{2}x-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{1}{8}-p)(b-\frac{-4}{12})& =(\color{red}{-p}+\color{orange}{\frac{1}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{3}p+\frac{1}{8}b+\frac{1}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-bp-\frac{1}{3}p+\frac{1}{8}b+\frac{1}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{9}{4})(\frac{2}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{9}b-\frac{9}{4}a+\frac{9}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =-ab+\frac{1}{9}b-\frac{9}{4}a+\frac{9}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{9}b-\frac{9}{4}a+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{3}{4}-a)(\frac{2}{20}-b)& =(\color{red}{-a}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{10}a-\frac{3}{4}b+\frac{3}{4}.\frac{1}{10}& \text{Uitwerken } \\ & =ab-\frac{1}{10}a-\frac{3}{4}b+\frac{3}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)