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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-15}{19})(b-\frac{-7}{2})& =(\color{red}{a}+\color{orange}{\frac{15}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{2}a+\frac{15}{19}b+\frac{15}{19}.\frac{7}{2}& \text{Uitwerken } \\ & =ab+\frac{7}{2}a+\frac{15}{19}b+\frac{105}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{8}-x)(p+\frac{14}{2})& =(\color{red}{-x}+\color{orange}{\frac{-7}{8}}).(\color{green}{p}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(7)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -px-7x-\frac{7}{8}p-\frac{7}{8}.7& \text{Uitwerken } \\ & =-px-7x-\frac{7}{8}p-\frac{49}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-2}{4})(\frac{-15}{20}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{4}q-\frac{1}{2}p-\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-pq-\frac{3}{4}q-\frac{1}{2}p-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{-16}{14})(a+\frac{17}{9})& =(\color{red}{x}+\color{orange}{\frac{-8}{7}}).(\color{green}{a}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{9}x-\frac{8}{7}a-\frac{8}{7}.\frac{17}{9}& \text{Uitwerken } \\ & =ax+\frac{17}{9}x-\frac{8}{7}a-\frac{136}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{3}{10})(x-\frac{18}{14})& =(\color{red}{b}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{7}b-\frac{3}{10}x+\frac{3}{10}.\frac{9}{7}& \text{Uitwerken } \\ & =bx-\frac{9}{7}b-\frac{3}{10}x+\frac{27}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{3}{2}-a)(x+\frac{-13}{19})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{13}{19}a+\frac{3}{2}x-\frac{3}{2}.\frac{13}{19}& \text{Uitwerken } \\ & =-ax+\frac{13}{19}a+\frac{3}{2}x-\frac{39}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{-8}{12})(\frac{7}{2}-b)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{-b}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{2}b-\frac{2}{3}b+\frac{2}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{2}+(\frac{-2}{3}))b+(\frac{-14}{6}) & \text{Neem samen} \\ &=-b^2+\frac{17}{6}b+(\frac{-14}{6}) & \text{Maak de som} \\ &=-b^2+\frac{17}{6}b+(\frac{-7}{3}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{9}+q)(b+\frac{-1}{20})& =(\color{red}{q}+\color{orange}{\frac{-17}{9}}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{20}q-\frac{17}{9}b+\frac{17}{9}.\frac{1}{20}& \text{Uitwerken } \\ & =bq-\frac{1}{20}q-\frac{17}{9}b+\frac{17}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{5}{8})(x-\frac{6}{11})& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{11}a+\frac{5}{8}x-\frac{5}{8}.\frac{6}{11}& \text{Uitwerken } \\ & =ax-\frac{6}{11}a+\frac{5}{8}x-\frac{30}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{6}{11}a+\frac{5}{8}x-\frac{15}{44} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-1}{11}+q)(p-\frac{11}{14})& =(\color{red}{q}+\color{orange}{\frac{-1}{11}}).(\color{green}{p}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{14}q-\frac{1}{11}p+\frac{1}{11}.\frac{11}{14}& \text{Uitwerken } \\ & =pq-\frac{11}{14}q-\frac{1}{11}p+\frac{11}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{11}{14}q-\frac{1}{11}p+\frac{1}{14} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-14}{4})(b+\frac{-1}{9})& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{9}p-\frac{7}{2}b+\frac{7}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =bp-\frac{1}{9}p-\frac{7}{2}b+\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{13}{17})(\frac{5}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{13}{17}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1q-\frac{13}{17}x+\frac{13}{17}.1& \text{Uitwerken } \\ & =-qx+1q-\frac{13}{17}x+\frac{13}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)