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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-8}{12})(\frac{-9}{17}+x)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{17}p+\frac{2}{3}x-\frac{2}{3}.\frac{9}{17}& \text{Uitwerken } \\ & =px-\frac{9}{17}p+\frac{2}{3}x-\frac{18}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{17}p+\frac{2}{3}x-\frac{6}{17} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{14}{13}+p)(\frac{10}{19}+x)& =(\color{red}{p}+\color{orange}{\frac{14}{13}}).(\color{green}{x}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{14}{13})} . \color{green}{(x)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{19}p+\frac{14}{13}x+\frac{14}{13}.\frac{10}{19}& \text{Uitwerken } \\ & =px+\frac{10}{19}p+\frac{14}{13}x+\frac{140}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{20}-a)((-11)+q)& =(\color{red}{-a}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{(-11)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-11)} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -aq+11a+\frac{3}{10}q-\frac{3}{10}.11& \text{Uitwerken } \\ & =-aq+11a+\frac{3}{10}q-\frac{33}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-17}{18}-a)(q-\frac{-17}{20})& =(\color{red}{-a}+\color{orange}{\frac{-17}{18}}).(\color{green}{q}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-17}{18})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{17}{20}a-\frac{17}{18}q-\frac{17}{18}.\frac{17}{20}& \text{Uitwerken } \\ & =-aq-\frac{17}{20}a-\frac{17}{18}q-\frac{289}{360} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{19}{4})(a-\frac{12}{6})& =(\color{red}{x}+\color{orange}{\frac{19}{4}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{4})} . \color{green}{(a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax-2x+\frac{19}{4}a-\frac{19}{4}.2& \text{Uitwerken } \\ & =ax-2x+\frac{19}{4}a-\frac{38}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-2x+\frac{19}{4}a-\frac{19}{2} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{14}{6})(\frac{-15}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{-x}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{5}{3}x-\frac{7}{3}x-\frac{7}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =-x^2+((\frac{-5}{3})+(\frac{-7}{3}))x-\frac{35}{9} & \text{Neem samen} \\ &=-x^2-\frac{12}{3}x-\frac{35}{9} & \text{Maak de som} \\ &=-x^2-4x-\frac{35}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(b+\frac{20}{6})(\frac{17}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{10}{3}}).(\color{green}{-p}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{10}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{2}b-\frac{10}{3}p+\frac{10}{3}.\frac{17}{2}& \text{Uitwerken } \\ & =-bp+\frac{17}{2}b-\frac{10}{3}p+\frac{170}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{17}{2}b-\frac{10}{3}p+\frac{85}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p-\frac{6}{8})(b-\frac{-2}{7})& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{7}p-\frac{3}{4}b-\frac{3}{4}.\frac{2}{7}& \text{Uitwerken } \\ & =bp+\frac{2}{7}p-\frac{3}{4}b-\frac{6}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{7}p-\frac{3}{4}b-\frac{3}{14} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{19}{6}+b)(\frac{-17}{6}+a)& =(\color{red}{b}+\color{orange}{\frac{19}{6}}).(\color{green}{a}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{6}b+\frac{19}{6}a-\frac{19}{6}.\frac{17}{6}& \text{Uitwerken } \\ & =ab-\frac{17}{6}b+\frac{19}{6}a-\frac{323}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{11}-p)(5-a)& =(\color{red}{-p}+\color{orange}{\frac{7}{11}}).(\color{green}{-a}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(5)} + \color{orange}{(\frac{7}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ap-5p-\frac{7}{11}a+\frac{7}{11}.5& \text{Uitwerken } \\ & =ap-5p-\frac{7}{11}a+\frac{35}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-13}{4})(p+\frac{-5}{10})& =(\color{red}{q}+\color{orange}{\frac{13}{4}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{13}{4})} . \color{green}{(p)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{2}q+\frac{13}{4}p-\frac{13}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =pq-\frac{1}{2}q+\frac{13}{4}p-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-17}{13})(p-\frac{-14}{5})& =(\color{red}{q}+\color{orange}{\frac{17}{13}}).(\color{green}{p}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{17}{13})} . \color{green}{(p)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{14}{5}q+\frac{17}{13}p+\frac{17}{13}.\frac{14}{5}& \text{Uitwerken } \\ & =pq+\frac{14}{5}q+\frac{17}{13}p+\frac{238}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)