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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{2}+x)(\frac{18}{18}-x)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -xx+1x-3x+3.1& \text{Uitwerken } \\ & =-x^2+(1+(-3))x+(-3) & \text{Neem samen} \\ &=-x^2-2x+(-3) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-3}{12}+a)(\frac{-14}{8}+x)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}a-\frac{1}{4}x+\frac{1}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}a-\frac{1}{4}x+\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{5}{9})(q-\frac{-5}{8})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{8}p-\frac{5}{9}q-\frac{5}{9}.\frac{5}{8}& \text{Uitwerken } \\ & =pq+\frac{5}{8}p-\frac{5}{9}q-\frac{25}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{3}{10})(\frac{-19}{20}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{-p}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{20}x-\frac{3}{10}p-\frac{3}{10}.\frac{19}{20}& \text{Uitwerken } \\ & =-px-\frac{19}{20}x-\frac{3}{10}p-\frac{57}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-3)(\frac{-12}{17}+a)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{17}b-3a+3.\frac{12}{17}& \text{Uitwerken } \\ & =ab-\frac{12}{17}b-3a+\frac{36}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{-10}{19})(\frac{-17}{7}+q)& =(\color{red}{b}+\color{orange}{\frac{10}{19}}).(\color{green}{q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{10}{19})} . \color{green}{(q)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{7}b+\frac{10}{19}q-\frac{10}{19}.\frac{17}{7}& \text{Uitwerken } \\ & =bq-\frac{17}{7}b+\frac{10}{19}q-\frac{170}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{9}{6}-q)(x+\frac{12}{15})& =(\color{red}{-q}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{5}q+\frac{3}{2}x+\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-qx-\frac{4}{5}q+\frac{3}{2}x+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{5}q+\frac{3}{2}x+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+\frac{-2}{10})(\frac{-16}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}p-\frac{1}{5}b+\frac{1}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}p-\frac{1}{5}b+\frac{4}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{17}{5}+q)(a-\frac{-14}{5})& =(\color{red}{q}+\color{orange}{\frac{17}{5}}).(\color{green}{a}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{17}{5})} . \color{green}{(a)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{5}q+\frac{17}{5}a+\frac{17}{5}.\frac{14}{5}& \text{Uitwerken } \\ & =aq+\frac{14}{5}q+\frac{17}{5}a+\frac{238}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{5}{7})(b+\frac{20}{20})& =(\color{red}{q}+\color{orange}{\frac{5}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1q+\frac{5}{7}b+\frac{5}{7}.1& \text{Uitwerken } \\ & =bq+1q+\frac{5}{7}b+\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{12}{20}+b)(a-\frac{16}{6})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{3}b+\frac{3}{5}a-\frac{3}{5}.\frac{8}{3}& \text{Uitwerken } \\ & =ab-\frac{8}{3}b+\frac{3}{5}a-\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{8}{3}b+\frac{3}{5}a-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{1}{8}+p)(\frac{6}{10}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{-p}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{5}p-\frac{1}{8}p+\frac{1}{8}.\frac{3}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{5}+(\frac{-1}{8}))p+(\frac{-3}{40}) & \text{Neem samen} \\ &=-p^2+\frac{19}{40}p+(\frac{-3}{40}) & \text{Maak de som} \\\end{align}\)