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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-9}{18}-b)(q+\frac{1}{18})& =(\color{red}{-b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{18})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{18}b-\frac{1}{2}q-\frac{1}{2}.\frac{1}{18}& \text{Uitwerken } \\ & =-bq-\frac{1}{18}b-\frac{1}{2}q-\frac{1}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{4}{15})(\frac{14}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{-4}{15}}).(\color{green}{-p}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{4}a+\frac{4}{15}p-\frac{4}{15}.\frac{7}{4}& \text{Uitwerken } \\ & =-ap+\frac{7}{4}a+\frac{4}{15}p-\frac{28}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{7}{4}a+\frac{4}{15}p-\frac{7}{15} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{14}{19}+a)(\frac{19}{6}-b)& =(\color{red}{a}+\color{orange}{\frac{14}{19}}).(\color{green}{-b}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{6}a-\frac{14}{19}b+\frac{14}{19}.\frac{19}{6}& \text{Uitwerken } \\ & =-ab+\frac{19}{6}a-\frac{14}{19}b+\frac{266}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{19}{6}a-\frac{14}{19}b+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-1}{19}+p)(\frac{9}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{19}}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{2}p+\frac{1}{19}b-\frac{1}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =-bp+\frac{1}{2}p+\frac{1}{19}b-\frac{1}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{9}+b)(\frac{4}{5}-q)& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{-q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{5}b+\frac{13}{9}q-\frac{13}{9}.\frac{4}{5}& \text{Uitwerken } \\ & =-bq+\frac{4}{5}b+\frac{13}{9}q-\frac{52}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-(-10))(\frac{-12}{7}+b)& =(\color{red}{p}+\color{orange}{10}).(\color{green}{b}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(10)} . \color{green}{(b)} + \color{orange}{(10)} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{12}{7}p+10b-10.\frac{12}{7}& \text{Uitwerken } \\ & =bp-\frac{12}{7}p+10b-\frac{120}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{20}{7})(q+\frac{18}{16})& =(\color{red}{x}+\color{orange}{\frac{-20}{7}}).(\color{green}{q}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{9}{8}x-\frac{20}{7}q-\frac{20}{7}.\frac{9}{8}& \text{Uitwerken } \\ & =qx+\frac{9}{8}x-\frac{20}{7}q-\frac{180}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{9}{8}x-\frac{20}{7}q-\frac{45}{14} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-3}{4}+a)(\frac{-16}{4}+q)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4a-\frac{3}{4}q+\frac{3}{4}.4& \text{Uitwerken } \\ & =aq-4a-\frac{3}{4}q+\frac{12}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4a-\frac{3}{4}q+3 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{7}+p)(p-\frac{-1}{6})& =(\color{red}{p}+\color{orange}{\frac{-18}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{6}p-\frac{18}{7}p-\frac{18}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =p^2+(\frac{1}{6}+(\frac{-18}{7}))p-(\frac{-18}{42}) & \text{Neem samen} \\ &=p^2-\frac{101}{42}p-(\frac{-18}{42}) & \text{Maak de som} \\ &=p^2-\frac{101}{42}p+\frac{3}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
10. \(\begin{align}(p-\frac{-5}{12})(p-\frac{-19}{2})& =(\color{red}{p}+\color{orange}{\frac{5}{12}}).(\color{green}{p}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{5}{12})} . \color{green}{(p)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{2}p+\frac{5}{12}p+\frac{5}{12}.\frac{19}{2}& \text{Uitwerken } \\ & =p^2+(\frac{19}{2}+\frac{5}{12})p+\frac{95}{24} & \text{Neem samen} \\ &=p^2+\frac{119}{12}p+\frac{95}{24} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b-\frac{14}{20})(\frac{-12}{6}+x)& =(\color{red}{b}+\color{orange}{\frac{-7}{10}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2b-\frac{7}{10}x+\frac{7}{10}.2& \text{Uitwerken } \\ & =bx-2b-\frac{7}{10}x+\frac{14}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-2b-\frac{7}{10}x+\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{11}{16})(a+\frac{7}{5})& =(\color{red}{q}+\color{orange}{\frac{11}{16}}).(\color{green}{a}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{5}q+\frac{11}{16}a+\frac{11}{16}.\frac{7}{5}& \text{Uitwerken } \\ & =aq+\frac{7}{5}q+\frac{11}{16}a+\frac{77}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)