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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{2}{14})(\frac{9}{5}+x)& =(\color{red}{a}+\color{orange}{\frac{-1}{7}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{5}a-\frac{1}{7}x-\frac{1}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =ax+\frac{9}{5}a-\frac{1}{7}x-\frac{9}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{4}-x)(a-\frac{4}{4})& =(\color{red}{-x}+\color{orange}{4}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x+4a-4.1& \text{Uitwerken } \\ & =-ax+1x+4a-4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-11}{15}+b)(p-\frac{-13}{16})& =(\color{red}{b}+\color{orange}{\frac{-11}{15}}).(\color{green}{p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{16}b-\frac{11}{15}p-\frac{11}{15}.\frac{13}{16}& \text{Uitwerken } \\ & =bp+\frac{13}{16}b-\frac{11}{15}p-\frac{143}{240} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{-11}{13})(\frac{-14}{15}-b)& =(\color{red}{b}+\color{orange}{\frac{-11}{13}}).(\color{green}{-b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{14}{15}b+\frac{11}{13}b+\frac{11}{13}.\frac{14}{15}& \text{Uitwerken } \\ & =-b^2+((\frac{-14}{15})+\frac{11}{13})b+(\frac{-154}{195}) & \text{Neem samen} \\ &=-b^2-\frac{17}{195}b+(\frac{-154}{195}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{-12}{10}+x)(\frac{11}{11}-q)& =(\color{red}{x}+\color{orange}{\frac{-6}{5}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x+\frac{6}{5}q-\frac{6}{5}.1& \text{Uitwerken } \\ & =-qx+1x+\frac{6}{5}q-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{-6}{12})(a+\frac{13}{17})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{17}p-\frac{1}{2}a-\frac{1}{2}.\frac{13}{17}& \text{Uitwerken } \\ & =ap+\frac{13}{17}p-\frac{1}{2}a-\frac{13}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{2}{2})(\frac{2}{16}-q)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{8}p+1q-1.\frac{1}{8}& \text{Uitwerken } \\ & =-pq+\frac{1}{8}p+1q-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{10}+x)(q+\frac{16}{15})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{15}x-1q-1.\frac{16}{15}& \text{Uitwerken } \\ & =qx+\frac{16}{15}x-1q-\frac{16}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{17}{19}+p)(\frac{9}{13}-q)& =(\color{red}{p}+\color{orange}{\frac{17}{19}}).(\color{green}{-q}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{13}p-\frac{17}{19}q+\frac{17}{19}.\frac{9}{13}& \text{Uitwerken } \\ & =-pq+\frac{9}{13}p-\frac{17}{19}q+\frac{153}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{11}{7}-b)(\frac{-11}{8}+a)& =(\color{red}{-b}+\color{orange}{\frac{11}{7}}).(\color{green}{a}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{11}{7})} . \color{green}{(a)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{11}{8}b+\frac{11}{7}a-\frac{11}{7}.\frac{11}{8}& \text{Uitwerken } \\ & =-ab+\frac{11}{8}b+\frac{11}{7}a-\frac{121}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{18}{8})(p+\frac{10}{6})& =(\color{red}{p}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{3}p+\frac{9}{4}p+\frac{9}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+(\frac{5}{3}+\frac{9}{4})p+\frac{45}{12} & \text{Neem samen} \\ &=p^2+\frac{47}{12}p+\frac{45}{12} & \text{Maak de som} \\ &=p^2+\frac{47}{12}p+\frac{15}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(b-\frac{-11}{8})(q-\frac{4}{20})& =(\color{red}{b}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}b+\frac{11}{8}q-\frac{11}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}b+\frac{11}{8}q-\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)