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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-7}{2}-q)(p+\frac{9}{4})& =(\color{red}{-q}+\color{orange}{\frac{-7}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{4}q-\frac{7}{2}p-\frac{7}{2}.\frac{9}{4}& \text{Uitwerken } \\ & =-pq-\frac{9}{4}q-\frac{7}{2}p-\frac{63}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{18}-q)(\frac{15}{13}-b)& =(\color{red}{-q}+\color{orange}{\frac{-1}{18}}).(\color{green}{-b}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{13}q+\frac{1}{18}b-\frac{1}{18}.\frac{15}{13}& \text{Uitwerken } \\ & =bq-\frac{15}{13}q+\frac{1}{18}b-\frac{15}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{15}{13}q+\frac{1}{18}b-\frac{5}{78} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{-16}{13})(\frac{-15}{15}+p)& =(\color{red}{a}+\color{orange}{\frac{-16}{13}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{16}{13}p+\frac{16}{13}.1& \text{Uitwerken } \\ & =ap-1a-\frac{16}{13}p+\frac{16}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-4}{6}+a)(\frac{8}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ab+1a+\frac{2}{3}b-\frac{2}{3}.1& \text{Uitwerken } \\ & =-ab+1a+\frac{2}{3}b-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{-11}{8})(b+(-15))& =(\color{red}{q}+\color{orange}{\frac{11}{8}}).(\color{green}{b}+\color{blue}{(-15)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-15)} + \color{orange}{(\frac{11}{8})} . \color{green}{(b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = bq-15q+\frac{11}{8}b-\frac{11}{8}.15& \text{Uitwerken } \\ & =bq-15q+\frac{11}{8}b-\frac{165}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{5}{13})(\frac{20}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{4}b+\frac{5}{13}a+\frac{5}{13}.\frac{5}{4}& \text{Uitwerken } \\ & =ab+\frac{5}{4}b+\frac{5}{13}a+\frac{25}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{15}{10}+x)(\frac{-14}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{14}{9}x+\frac{3}{2}x-\frac{3}{2}.\frac{14}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-14}{9})+\frac{3}{2})x-(\frac{-42}{18}) & \text{Neem samen} \\ &=x^2-\frac{1}{18}x-(\frac{-42}{18}) & \text{Maak de som} \\ &=x^2-\frac{1}{18}x+\frac{7}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(b+\frac{16}{11})(\frac{-3}{8}-x)& =(\color{red}{b}+\color{orange}{\frac{16}{11}}).(\color{green}{-x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{16}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{8}b-\frac{16}{11}x-\frac{16}{11}.\frac{3}{8}& \text{Uitwerken } \\ & =-bx-\frac{3}{8}b-\frac{16}{11}x-\frac{48}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{8}b-\frac{16}{11}x-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{1}{3}-q)(q+\frac{7}{17})& =(\color{red}{-q}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{7}{17}q+\frac{1}{3}q+\frac{1}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =-q^2+((\frac{-7}{17})+\frac{1}{3})q+(\frac{-7}{51}) & \text{Neem samen} \\ &=-q^2-\frac{4}{51}q+(\frac{-7}{51}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q-\frac{9}{9})(p-\frac{-6}{11})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{11}q-1p-1.\frac{6}{11}& \text{Uitwerken } \\ & =pq+\frac{6}{11}q-1p-\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-15}{7}+q)(\frac{-14}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q-\frac{15}{7}p+\frac{15}{7}.1& \text{Uitwerken } \\ & =pq-1q-\frac{15}{7}p+\frac{15}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{18}{8})(b-\frac{11}{15})& =(\color{red}{x}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{15}x+\frac{9}{4}b-\frac{9}{4}.\frac{11}{15}& \text{Uitwerken } \\ & =bx-\frac{11}{15}x+\frac{9}{4}b-\frac{99}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{11}{15}x+\frac{9}{4}b-\frac{33}{20} & \text{Vereenvoudig} \\\end{align}\)