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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{9}{8})(\frac{9}{3}+a)& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3p-\frac{9}{8}a-\frac{9}{8}.3& \text{Uitwerken } \\ & =ap+3p-\frac{9}{8}a-\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{7}{20}+a)(\frac{-19}{20}-x)& =(\color{red}{a}+\color{orange}{\frac{7}{20}}).(\color{green}{-x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{7}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{19}{20}a-\frac{7}{20}x-\frac{7}{20}.\frac{19}{20}& \text{Uitwerken } \\ & =-ax-\frac{19}{20}a-\frac{7}{20}x-\frac{133}{400} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-3}{20})(\frac{-13}{10}-p)& =(\color{red}{x}+\color{orange}{\frac{3}{20}}).(\color{green}{-p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{3}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{10}x-\frac{3}{20}p-\frac{3}{20}.\frac{13}{10}& \text{Uitwerken } \\ & =-px-\frac{13}{10}x-\frac{3}{20}p-\frac{39}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-12}{4}-x)(\frac{15}{20}+p)& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{4}x-3p-3.\frac{3}{4}& \text{Uitwerken } \\ & =-px-\frac{3}{4}x-3p-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{2}{20}-q)(\frac{13}{8}+p)& =(\color{red}{-q}+\color{orange}{\frac{1}{10}}).(\color{green}{p}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{8}q+\frac{1}{10}p+\frac{1}{10}.\frac{13}{8}& \text{Uitwerken } \\ & =-pq-\frac{13}{8}q+\frac{1}{10}p+\frac{13}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{9}{6}+x)(\frac{-18}{15}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{5}x+\frac{3}{2}x-\frac{3}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{5})+\frac{3}{2})x-(\frac{-18}{10}) & \text{Neem samen} \\ &=x^2+\frac{3}{10}x-(\frac{-18}{10}) & \text{Maak de som} \\ &=x^2+\frac{3}{10}x+\frac{9}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(\frac{-8}{18}+p)(b+\frac{18}{9})& =(\color{red}{p}+\color{orange}{\frac{-4}{9}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p-\frac{4}{9}b-\frac{4}{9}.2& \text{Uitwerken } \\ & =bp+2p-\frac{4}{9}b-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-15}{14})(b-(-12))& =(\color{red}{p}+\color{orange}{\frac{-15}{14}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(12)} + \color{orange}{(\frac{-15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bp+12p-\frac{15}{14}b-\frac{15}{14}.12& \text{Uitwerken } \\ & =bp+12p-\frac{15}{14}b-\frac{180}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+12p-\frac{15}{14}b-\frac{90}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x-\frac{-5}{7})(q-\frac{19}{16})& =(\color{red}{x}+\color{orange}{\frac{5}{7}}).(\color{green}{q}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{16}x+\frac{5}{7}q-\frac{5}{7}.\frac{19}{16}& \text{Uitwerken } \\ & =qx-\frac{19}{16}x+\frac{5}{7}q-\frac{95}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-11}{12})(\frac{5}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{-11}{12}}).(\color{green}{a}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{8}a-\frac{11}{12}a-\frac{11}{12}.\frac{5}{8}& \text{Uitwerken } \\ & =a^2+(\frac{5}{8}+(\frac{-11}{12}))a-(\frac{-55}{96}) & \text{Neem samen} \\ &=a^2-\frac{7}{24}a-(\frac{-55}{96}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{19}{5}-q)(\frac{-19}{14}+x)& =(\color{red}{-q}+\color{orange}{\frac{19}{5}}).(\color{green}{x}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{19}{5})} . \color{green}{(x)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{14}q+\frac{19}{5}x-\frac{19}{5}.\frac{19}{14}& \text{Uitwerken } \\ & =-qx+\frac{19}{14}q+\frac{19}{5}x-\frac{361}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{9}{2})(a+\frac{4}{6})& =(\color{red}{x}+\color{orange}{\frac{9}{2}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{9}{2})} . \color{green}{(a)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x+\frac{9}{2}a+\frac{9}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x+\frac{9}{2}a+\frac{18}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{3}x+\frac{9}{2}a+3 & \text{Vereenvoudig} \\\end{align}\)