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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{10}+a)(a+\frac{5}{10})& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{2}a-\frac{3}{2}a-\frac{3}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+(\frac{1}{2}+(\frac{-3}{2}))a-(\frac{-3}{4}) & \text{Neem samen} \\ &=a^2-\frac{2}{2}a-(\frac{-3}{4}) & \text{Maak de som} \\ &=a^2-1a+\frac{3}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(\frac{9}{11}-x)(\frac{-1}{2}-a)& =(\color{red}{-x}+\color{orange}{\frac{9}{11}}).(\color{green}{-a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{9}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x-\frac{9}{11}a-\frac{9}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x-\frac{9}{11}a-\frac{9}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{6}-x)(\frac{19}{5}-p)& =(\color{red}{-x}+\color{orange}{\frac{-7}{6}}).(\color{green}{-p}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{5}x+\frac{7}{6}p-\frac{7}{6}.\frac{19}{5}& \text{Uitwerken } \\ & =px-\frac{19}{5}x+\frac{7}{6}p-\frac{133}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{18}{18})(\frac{-14}{15}+b)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{14}{15}x+1b-1.\frac{14}{15}& \text{Uitwerken } \\ & =bx-\frac{14}{15}x+1b-\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-1)(\frac{-7}{13}-q)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{13}x+1q+1.\frac{7}{13}& \text{Uitwerken } \\ & =-qx-\frac{7}{13}x+1q+\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-15}{18}+p)(\frac{20}{20}-b)& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1p+\frac{5}{6}b-\frac{5}{6}.1& \text{Uitwerken } \\ & =-bp+1p+\frac{5}{6}b-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{18}{3})(q+\frac{-10}{8})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{4}x+6q-6.\frac{5}{4}& \text{Uitwerken } \\ & =qx-\frac{5}{4}x+6q-\frac{30}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{4}x+6q-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{1}{2}-a)(x+\frac{7}{12})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{12}a+\frac{1}{2}x+\frac{1}{2}.\frac{7}{12}& \text{Uitwerken } \\ & =-ax-\frac{7}{12}a+\frac{1}{2}x+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(19+q)(\frac{19}{8}+p)& =(\color{red}{q}+\color{orange}{19}).(\color{green}{p}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(19)} . \color{green}{(p)} + \color{orange}{(19)} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{8}q+19p+19.\frac{19}{8}& \text{Uitwerken } \\ & =pq+\frac{19}{8}q+19p+\frac{361}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{1}{2}-q)(b+\frac{4}{14})& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{7}q+\frac{1}{2}b+\frac{1}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =-bq-\frac{2}{7}q+\frac{1}{2}b+\frac{2}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{2}{7}q+\frac{1}{2}b+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{18}{12}-b)(p+\frac{4}{9})& =(\color{red}{-b}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{9}b+\frac{3}{2}p+\frac{3}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-bp-\frac{4}{9}b+\frac{3}{2}p+\frac{12}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{9}b+\frac{3}{2}p+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{12}+x)(\frac{18}{20}+q)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{10}x-\frac{5}{4}q-\frac{5}{4}.\frac{9}{10}& \text{Uitwerken } \\ & =qx+\frac{9}{10}x-\frac{5}{4}q-\frac{45}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{10}x-\frac{5}{4}q-\frac{9}{8} & \text{Vereenvoudig} \\\end{align}\)