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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{18}-q)(\frac{18}{15}-q)& =(\color{red}{-q}+\color{orange}{\frac{-5}{18}}).(\color{green}{-q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{6}{5}q+\frac{5}{18}q-\frac{5}{18}.\frac{6}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-6}{5})+\frac{5}{18})q-(\frac{-30}{90}) & \text{Neem samen} \\ &=q^2-\frac{83}{90}q-(\frac{-30}{90}) & \text{Maak de som} \\ &=q^2-\frac{83}{90}q+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(x-\frac{-5}{18})(\frac{-7}{15}-a)& =(\color{red}{x}+\color{orange}{\frac{5}{18}}).(\color{green}{-a}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{15}x-\frac{5}{18}a-\frac{5}{18}.\frac{7}{15}& \text{Uitwerken } \\ & =-ax-\frac{7}{15}x-\frac{5}{18}a-\frac{35}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{15}x-\frac{5}{18}a-\frac{7}{54} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{-17}{13})(\frac{4}{14}+x)& =(\color{red}{b}+\color{orange}{\frac{17}{13}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{17}{13})} . \color{green}{(x)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{7}b+\frac{17}{13}x+\frac{17}{13}.\frac{2}{7}& \text{Uitwerken } \\ & =bx+\frac{2}{7}b+\frac{17}{13}x+\frac{34}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{10}{18})(\frac{-11}{8}+p)& =(\color{red}{x}+\color{orange}{\frac{5}{9}}).(\color{green}{p}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{5}{9})} . \color{green}{(p)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{8}x+\frac{5}{9}p-\frac{5}{9}.\frac{11}{8}& \text{Uitwerken } \\ & =px-\frac{11}{8}x+\frac{5}{9}p-\frac{55}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{3}{17})((-13)-a)& =(\color{red}{b}+\color{orange}{\frac{3}{17}}).(\color{green}{-a}+\color{blue}{(-13)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-13)} + \color{orange}{(\frac{3}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -ab-13b-\frac{3}{17}a-\frac{3}{17}.13& \text{Uitwerken } \\ & =-ab-13b-\frac{3}{17}a-\frac{39}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{20}{2}-x)(\frac{8}{15}+q)& =(\color{red}{-x}+\color{orange}{10}).(\color{green}{q}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(10)} . \color{green}{(q)} + \color{orange}{(10)} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{15}x+10q+10.\frac{8}{15}& \text{Uitwerken } \\ & =-qx-\frac{8}{15}x+10q+\frac{80}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{8}{15}x+10q+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x-\frac{-2}{11})(b+\frac{-14}{2})& =(\color{red}{x}+\color{orange}{\frac{2}{11}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-7)} + \color{orange}{(\frac{2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bx-7x+\frac{2}{11}b-\frac{2}{11}.7& \text{Uitwerken } \\ & =bx-7x+\frac{2}{11}b-\frac{14}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{2}{3})(x-\frac{3}{16})& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{16}p+\frac{2}{3}x-\frac{2}{3}.\frac{3}{16}& \text{Uitwerken } \\ & =px-\frac{3}{16}p+\frac{2}{3}x-\frac{6}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{16}p+\frac{2}{3}x-\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{5}{20})(p+\frac{3}{17})& =(\color{red}{x}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{17}x-\frac{1}{4}p-\frac{1}{4}.\frac{3}{17}& \text{Uitwerken } \\ & =px+\frac{3}{17}x-\frac{1}{4}p-\frac{3}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-20}{15}-b)(\frac{2}{9}-b)& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{9}b+\frac{4}{3}b-\frac{4}{3}.\frac{2}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{9})+\frac{4}{3})b-(\frac{-8}{27}) & \text{Neem samen} \\ &=b^2+\frac{10}{9}b-(\frac{-8}{27}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-13}{19}-b)(\frac{15}{2}+x)& =(\color{red}{-b}+\color{orange}{\frac{-13}{19}}).(\color{green}{x}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{2}b-\frac{13}{19}x-\frac{13}{19}.\frac{15}{2}& \text{Uitwerken } \\ & =-bx-\frac{15}{2}b-\frac{13}{19}x-\frac{195}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-13}{3})(\frac{-10}{10}-b)& =(\color{red}{p}+\color{orange}{\frac{-13}{3}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p+\frac{13}{3}b+\frac{13}{3}.1& \text{Uitwerken } \\ & =-bp-1p+\frac{13}{3}b+\frac{13}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)