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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{18}{8}+q)(x+\frac{4}{2})& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{4})} . \color{green}{(x)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qx+2q+\frac{9}{4}x+\frac{9}{4}.2& \text{Uitwerken } \\ & =qx+2q+\frac{9}{4}x+\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+2q+\frac{9}{4}x+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{9}-b)(q-\frac{12}{13})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{12}{13}b-1q+1.\frac{12}{13}& \text{Uitwerken } \\ & =-bq+\frac{12}{13}b-1q+\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{18}{3})(\frac{-1}{10}-p)& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{-p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(-6)} . \color{green}{(-p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{10}b+6p+6.\frac{1}{10}& \text{Uitwerken } \\ & =-bp-\frac{1}{10}b+6p+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{10}b+6p+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-12}{10}-x)(p+\frac{11}{12})& =(\color{red}{-x}+\color{orange}{\frac{-6}{5}}).(\color{green}{p}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{11}{12}x-\frac{6}{5}p-\frac{6}{5}.\frac{11}{12}& \text{Uitwerken } \\ & =-px-\frac{11}{12}x-\frac{6}{5}p-\frac{66}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{11}{12}x-\frac{6}{5}p-\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{17}{18}+q)(\frac{-19}{11}+q)& =(\color{red}{q}+\color{orange}{\frac{17}{18}}).(\color{green}{q}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{17}{18})} . \color{green}{(q)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{11}q+\frac{17}{18}q-\frac{17}{18}.\frac{19}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{11})+\frac{17}{18})q-(\frac{-323}{198}) & \text{Neem samen} \\ &=q^2-\frac{155}{198}q-(\frac{-323}{198}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{20}{18}+a)(p+\frac{1}{10})& =(\color{red}{a}+\color{orange}{\frac{10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{10}a+\frac{10}{9}p+\frac{10}{9}.\frac{1}{10}& \text{Uitwerken } \\ & =ap+\frac{1}{10}a+\frac{10}{9}p+\frac{10}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{10}a+\frac{10}{9}p+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{15}{3})(x+\frac{20}{4})& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx+5q-5x-5.5& \text{Uitwerken } \\ & =qx+5q-5x-25 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-14}{16}+p)(\frac{-13}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{17}p-\frac{7}{8}q+\frac{7}{8}.\frac{13}{17}& \text{Uitwerken } \\ & =pq-\frac{13}{17}p-\frac{7}{8}q+\frac{91}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{4}{17})(p+\frac{16}{19})& =(\color{red}{a}+\color{orange}{\frac{4}{17}}).(\color{green}{p}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{19}a+\frac{4}{17}p+\frac{4}{17}.\frac{16}{19}& \text{Uitwerken } \\ & =ap+\frac{16}{19}a+\frac{4}{17}p+\frac{64}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-9}{17}-p)(\frac{12}{14}-x)& =(\color{red}{-p}+\color{orange}{\frac{-9}{17}}).(\color{green}{-x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{7}p+\frac{9}{17}x-\frac{9}{17}.\frac{6}{7}& \text{Uitwerken } \\ & =px-\frac{6}{7}p+\frac{9}{17}x-\frac{54}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-10}{18})(q-\frac{-15}{6})& =(\color{red}{p}+\color{orange}{\frac{5}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{2}p+\frac{5}{9}q+\frac{5}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =pq+\frac{5}{2}p+\frac{5}{9}q+\frac{25}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{10}{4}+p)(p+8)& =(\color{red}{p}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{8})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(8)} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = pp+8p+\frac{5}{2}p+\frac{5}{2}.8& \text{Uitwerken } \\ & =p^2+(8+\frac{5}{2})p+\frac{40}{2} & \text{Neem samen} \\ &=p^2+\frac{21}{2}p+\frac{40}{2} & \text{Maak de som} \\ &=p^2+\frac{21}{2}p+20 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)