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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{20}-p)(\frac{20}{13}-a)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{13}p+1a-1.\frac{20}{13}& \text{Uitwerken } \\ & =ap-\frac{20}{13}p+1a-\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{4}{7})(p-\frac{8}{12})& =(\color{red}{a}+\color{orange}{\frac{4}{7}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}a+\frac{4}{7}p-\frac{4}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}a+\frac{4}{7}p-\frac{8}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{7}{8}+b)(b-\frac{-5}{17})& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{17}b+\frac{7}{8}b+\frac{7}{8}.\frac{5}{17}& \text{Uitwerken } \\ & =b^2+(\frac{5}{17}+\frac{7}{8})b+\frac{35}{136} & \text{Neem samen} \\ &=b^2+\frac{159}{136}b+\frac{35}{136} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(x+\frac{9}{15})(\frac{-14}{12}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{-p}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{6}x-\frac{3}{5}p-\frac{3}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =-px-\frac{7}{6}x-\frac{3}{5}p-\frac{21}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{6}x-\frac{3}{5}p-\frac{7}{10} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(q+\frac{14}{16})(\frac{4}{12}-b)& =(\color{red}{q}+\color{orange}{\frac{7}{8}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{3}q-\frac{7}{8}b+\frac{7}{8}.\frac{1}{3}& \text{Uitwerken } \\ & =-bq+\frac{1}{3}q-\frac{7}{8}b+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{8}{18})(b-\frac{-2}{3})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}a+\frac{4}{9}b+\frac{4}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}a+\frac{4}{9}b+\frac{8}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{15}{20})(\frac{-6}{11}-b)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-b}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{11}q-\frac{3}{4}b-\frac{3}{4}.\frac{6}{11}& \text{Uitwerken } \\ & =-bq-\frac{6}{11}q-\frac{3}{4}b-\frac{18}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{6}{11}q-\frac{3}{4}b-\frac{9}{22} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(q+\frac{3}{19})(x+\frac{14}{2})& =(\color{red}{q}+\color{orange}{\frac{3}{19}}).(\color{green}{x}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(7)} + \color{orange}{(\frac{3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = qx+7q+\frac{3}{19}x+\frac{3}{19}.7& \text{Uitwerken } \\ & =qx+7q+\frac{3}{19}x+\frac{21}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-16}{14})(p+\frac{4}{15})& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{15}b-\frac{8}{7}p-\frac{8}{7}.\frac{4}{15}& \text{Uitwerken } \\ & =bp+\frac{4}{15}b-\frac{8}{7}p-\frac{32}{105} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-\frac{6}{13})(p+\frac{-1}{4})& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{4}a-\frac{6}{13}p+\frac{6}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =ap-\frac{1}{4}a-\frac{6}{13}p+\frac{6}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{4}a-\frac{6}{13}p+\frac{3}{26} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x+\frac{-3}{20})(p-\frac{-13}{7})& =(\color{red}{x}+\color{orange}{\frac{-3}{20}}).(\color{green}{p}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{7}x-\frac{3}{20}p-\frac{3}{20}.\frac{13}{7}& \text{Uitwerken } \\ & =px+\frac{13}{7}x-\frac{3}{20}p-\frac{39}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-17}{20}-q)(\frac{20}{3}+x)& =(\color{red}{-q}+\color{orange}{\frac{-17}{20}}).(\color{green}{x}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{3}q-\frac{17}{20}x-\frac{17}{20}.\frac{20}{3}& \text{Uitwerken } \\ & =-qx-\frac{20}{3}q-\frac{17}{20}x-\frac{340}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{20}{3}q-\frac{17}{20}x-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)