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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{4}{16})(\frac{18}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b-\frac{1}{4}p+\frac{1}{4}.1& \text{Uitwerken } \\ & =-bp+1b-\frac{1}{4}p+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{11}{8}-p)(\frac{2}{2}-b)& =(\color{red}{-p}+\color{orange}{\frac{11}{8}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{11}{8}b+\frac{11}{8}.1& \text{Uitwerken } \\ & =bp-1p-\frac{11}{8}b+\frac{11}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-14}{16}-b)(x-\frac{7}{4})& =(\color{red}{-b}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{4}b-\frac{7}{8}x+\frac{7}{8}.\frac{7}{4}& \text{Uitwerken } \\ & =-bx+\frac{7}{4}b-\frac{7}{8}x+\frac{49}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{-3}{4})(\frac{-8}{16}-q)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}p+\frac{3}{4}q+\frac{3}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}p+\frac{3}{4}q+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{10}-x)(\frac{18}{6}+p)& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -px-3x+\frac{3}{5}p+\frac{3}{5}.3& \text{Uitwerken } \\ & =-px-3x+\frac{3}{5}p+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{3}+b)(\frac{-12}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{4}b-\frac{2}{3}p+\frac{2}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =bp-\frac{3}{4}b-\frac{2}{3}p+\frac{6}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{4}b-\frac{2}{3}p+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x-\frac{-19}{16})(\frac{1}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{19}{16}}).(\color{green}{-a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{19}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{14}x-\frac{19}{16}a+\frac{19}{16}.\frac{1}{14}& \text{Uitwerken } \\ & =-ax+\frac{1}{14}x-\frac{19}{16}a+\frac{19}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-16}{3}+q)(\frac{16}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{-16}{3}}).(\color{green}{-a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{8}{3}q+\frac{16}{3}a-\frac{16}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =-aq+\frac{8}{3}q+\frac{16}{3}a-\frac{128}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{-6}{2})(\frac{16}{11}-a)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{11}q-3a+3.\frac{16}{11}& \text{Uitwerken } \\ & =-aq+\frac{16}{11}q-3a+\frac{48}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{2}-p)(a-\frac{-13}{13})& =(\color{red}{-p}+\color{orange}{4}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1p+4a+4.1& \text{Uitwerken } \\ & =-ap-1p+4a+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-17}{4})(a-\frac{11}{10})& =(\color{red}{p}+\color{orange}{\frac{-17}{4}}).(\color{green}{a}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{10}p-\frac{17}{4}a+\frac{17}{4}.\frac{11}{10}& \text{Uitwerken } \\ & =ap-\frac{11}{10}p-\frac{17}{4}a+\frac{187}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{11}{14}+x)(\frac{7}{12}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{14}}).(\color{green}{-a}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{11}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{12}x-\frac{11}{14}a+\frac{11}{14}.\frac{7}{12}& \text{Uitwerken } \\ & =-ax+\frac{7}{12}x-\frac{11}{14}a+\frac{77}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{12}x-\frac{11}{14}a+\frac{11}{24} & \text{Vereenvoudig} \\\end{align}\)