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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{2}{9})(\frac{18}{15}-b)& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{-b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{2}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{6}{5}q-\frac{2}{9}b+\frac{2}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =-bq+\frac{6}{5}q-\frac{2}{9}b+\frac{12}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{6}{5}q-\frac{2}{9}b+\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{9}-x)(\frac{2}{14}+p)& =(\color{red}{-x}+\color{orange}{\frac{-8}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{7}x-\frac{8}{9}p-\frac{8}{9}.\frac{1}{7}& \text{Uitwerken } \\ & =-px-\frac{1}{7}x-\frac{8}{9}p-\frac{8}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{-2}{14})(q+\frac{-2}{12})& =(\color{red}{q}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{6}q-\frac{1}{7}q+\frac{1}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{6})+(\frac{-1}{7}))q+\frac{1}{42} & \text{Neem samen} \\ &=q^2-\frac{13}{42}q+\frac{1}{42} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{15}-b)(\frac{5}{15}-q)& =(\color{red}{-b}+\color{orange}{\frac{-2}{15}}).(\color{green}{-q}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}b+\frac{2}{15}q-\frac{2}{15}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}b+\frac{2}{15}q-\frac{2}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-1}{17})(q+\frac{-20}{4})& =(\color{red}{x}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5x+\frac{1}{17}q-\frac{1}{17}.5& \text{Uitwerken } \\ & =qx-5x+\frac{1}{17}q-\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{14}{2}+a)(\frac{-8}{17}+p)& =(\color{red}{a}+\color{orange}{7}).(\color{green}{p}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(7)} . \color{green}{(p)} + \color{orange}{(7)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{17}a+7p-7.\frac{8}{17}& \text{Uitwerken } \\ & =ap-\frac{8}{17}a+7p-\frac{56}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{-12}{17})(a-\frac{-5}{8})& =(\color{red}{p}+\color{orange}{\frac{-12}{17}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{8}p-\frac{12}{17}a-\frac{12}{17}.\frac{5}{8}& \text{Uitwerken } \\ & =ap+\frac{5}{8}p-\frac{12}{17}a-\frac{60}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{8}p-\frac{12}{17}a-\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b+\frac{15}{3})(p+\frac{-19}{17})& =(\color{red}{b}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{17}b+5p-5.\frac{19}{17}& \text{Uitwerken } \\ & =bp-\frac{19}{17}b+5p-\frac{95}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{14}{10})(q+(-14))& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{q}+\color{blue}{(-14)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-14)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = qx-14x-\frac{7}{5}q+\frac{7}{5}.14& \text{Uitwerken } \\ & =qx-14x-\frac{7}{5}q+\frac{98}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{2}{8}-a)(a-\frac{-9}{10})& =(\color{red}{-a}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{10}a+\frac{1}{4}a+\frac{1}{4}.\frac{9}{10}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{10})+\frac{1}{4})a+(\frac{-9}{40}) & \text{Neem samen} \\ &=-a^2-\frac{13}{20}a+(\frac{-9}{40}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(p-\frac{-17}{7})(\frac{-10}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{17}{7}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{17}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{2}p-\frac{17}{7}x-\frac{17}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =-px-\frac{5}{2}p-\frac{17}{7}x-\frac{85}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{5}{19})(\frac{9}{6}+x)& =(\color{red}{x}+\color{orange}{\frac{5}{19}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{5}{19})} . \color{green}{(x)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{2}x+\frac{5}{19}x+\frac{5}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =x^2+(\frac{3}{2}+\frac{5}{19})x+\frac{15}{38} & \text{Neem samen} \\ &=x^2+\frac{67}{38}x+\frac{15}{38} & \text{Maak de som} \\\end{align}\)