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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-1}{6})(\frac{10}{16}-b)& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{-b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{8}x+\frac{1}{6}b-\frac{1}{6}.\frac{5}{8}& \text{Uitwerken } \\ & =-bx+\frac{5}{8}x+\frac{1}{6}b-\frac{5}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{17}{19})(b-\frac{4}{12})& =(\color{red}{q}+\color{orange}{\frac{-17}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q-\frac{17}{19}b+\frac{17}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q-\frac{17}{19}b+\frac{17}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{9}-p)(\frac{-12}{9}+a)& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{3}p+\frac{2}{3}a-\frac{2}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =-ap+\frac{4}{3}p+\frac{2}{3}a-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(11-a)(q-\frac{8}{12})& =(\color{red}{-a}+\color{orange}{11}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(11)} . \color{green}{(q)} + \color{orange}{(11)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}a+11q-11.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}a+11q-\frac{22}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{11}+q)(\frac{-13}{12}+p)& =(\color{red}{q}+\color{orange}{\frac{-6}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{12}q-\frac{6}{11}p+\frac{6}{11}.\frac{13}{12}& \text{Uitwerken } \\ & =pq-\frac{13}{12}q-\frac{6}{11}p+\frac{78}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{13}{12}q-\frac{6}{11}p+\frac{13}{22} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{19}{14})(\frac{11}{7}-b)& =(\color{red}{b}+\color{orange}{\frac{19}{14}}).(\color{green}{-b}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(\frac{19}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{7}b-\frac{19}{14}b+\frac{19}{14}.\frac{11}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{7}+(\frac{-19}{14}))b+(\frac{-209}{98}) & \text{Neem samen} \\ &=-b^2+\frac{3}{14}b+(\frac{-209}{98}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{20}-q)(p+\frac{14}{16})& =(\color{red}{-q}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{7}{8}q-\frac{11}{20}p-\frac{11}{20}.\frac{7}{8}& \text{Uitwerken } \\ & =-pq-\frac{7}{8}q-\frac{11}{20}p-\frac{77}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{11}{19}+x)(b+\frac{-12}{15})& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{5}x+\frac{11}{19}b-\frac{11}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =bx-\frac{4}{5}x+\frac{11}{19}b-\frac{44}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{10}{19})(\frac{4}{4}+b)& =(\color{red}{q}+\color{orange}{\frac{10}{19}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{10}{19})} . \color{green}{(b)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{10}{19}b+\frac{10}{19}.1& \text{Uitwerken } \\ & =bq+1q+\frac{10}{19}b+\frac{10}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{10}{8})(x+\frac{-8}{10})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{5}x-\frac{5}{4}x+\frac{5}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{5})+(\frac{-5}{4}))x+\frac{20}{20} & \text{Neem samen} \\ &=x^2-\frac{41}{20}x+\frac{20}{20} & \text{Maak de som} \\ &=x^2-\frac{41}{20}x+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{6}-x)(b+\frac{3}{18})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{6}x-\frac{1}{2}b-\frac{1}{2}.\frac{1}{6}& \text{Uitwerken } \\ & =-bx-\frac{1}{6}x-\frac{1}{2}b-\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{-14}{13})(\frac{10}{15}-a)& =(\color{red}{x}+\color{orange}{\frac{14}{13}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{14}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{3}x-\frac{14}{13}a+\frac{14}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax+\frac{2}{3}x-\frac{14}{13}a+\frac{28}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)