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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-16}{8})(\frac{-17}{16}-p)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{16}a+2p+2.\frac{17}{16}& \text{Uitwerken } \\ & =-ap-\frac{17}{16}a+2p+\frac{34}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{17}{16}a+2p+\frac{17}{8} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{11}-a)(\frac{-14}{18}+p)& =(\color{red}{-a}+\color{orange}{\frac{-10}{11}}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{9}a-\frac{10}{11}p+\frac{10}{11}.\frac{7}{9}& \text{Uitwerken } \\ & =-ap+\frac{7}{9}a-\frac{10}{11}p+\frac{70}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-12}{8}+x)(q-\frac{-16}{9})& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{9}x-\frac{3}{2}q-\frac{3}{2}.\frac{16}{9}& \text{Uitwerken } \\ & =qx+\frac{16}{9}x-\frac{3}{2}q-\frac{48}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{16}{9}x-\frac{3}{2}q-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-12}{17}+x)(a-4)& =(\color{red}{x}+\color{orange}{\frac{-12}{17}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ax-4x-\frac{12}{17}a+\frac{12}{17}.4& \text{Uitwerken } \\ & =ax-4x-\frac{12}{17}a+\frac{48}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-12}{15})(\frac{4}{17}-a)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{-a}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{17}x-\frac{4}{5}a+\frac{4}{5}.\frac{4}{17}& \text{Uitwerken } \\ & =-ax+\frac{4}{17}x-\frac{4}{5}a+\frac{16}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-5}{16}-a)(\frac{19}{14}-x)& =(\color{red}{-a}+\color{orange}{\frac{-5}{16}}).(\color{green}{-x}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{14}a+\frac{5}{16}x-\frac{5}{16}.\frac{19}{14}& \text{Uitwerken } \\ & =ax-\frac{19}{14}a+\frac{5}{16}x-\frac{95}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-5}{6}+q)(p-\frac{18}{3})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{p}+\color{blue}{(-6)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-6)} + \color{orange}{(\frac{-5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = pq-6q-\frac{5}{6}p+\frac{5}{6}.6& \text{Uitwerken } \\ & =pq-6q-\frac{5}{6}p+\frac{30}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-6q-\frac{5}{6}p+5 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-8}{6}+p)(b-\frac{-2}{8})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}p-\frac{4}{3}b-\frac{4}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}p-\frac{4}{3}b-\frac{4}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{4}p-\frac{4}{3}b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x+\frac{-13}{15})(q-\frac{-13}{8})& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{q}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{8}x-\frac{13}{15}q-\frac{13}{15}.\frac{13}{8}& \text{Uitwerken } \\ & =qx+\frac{13}{8}x-\frac{13}{15}q-\frac{169}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{9}-a)(\frac{-16}{13}-p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{13}a+\frac{1}{3}p+\frac{1}{3}.\frac{16}{13}& \text{Uitwerken } \\ & =ap+\frac{16}{13}a+\frac{1}{3}p+\frac{16}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-13}{3}-x)(a-\frac{5}{13})& =(\color{red}{-x}+\color{orange}{\frac{-13}{3}}).(\color{green}{a}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{13}x-\frac{13}{3}a+\frac{13}{3}.\frac{5}{13}& \text{Uitwerken } \\ & =-ax+\frac{5}{13}x-\frac{13}{3}a+\frac{65}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{13}x-\frac{13}{3}a+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-2}{10}+b)(a-\frac{18}{9})& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b-\frac{1}{5}a+\frac{1}{5}.2& \text{Uitwerken } \\ & =ab-2b-\frac{1}{5}a+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)