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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-13}{7})(\frac{-6}{6}+b)& =(\color{red}{a}+\color{orange}{\frac{-13}{7}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a-\frac{13}{7}b+\frac{13}{7}.1& \text{Uitwerken } \\ & =ab-1a-\frac{13}{7}b+\frac{13}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{13}{20})(p+\frac{13}{15})& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{p}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{15}x-\frac{13}{20}p-\frac{13}{20}.\frac{13}{15}& \text{Uitwerken } \\ & =px+\frac{13}{15}x-\frac{13}{20}p-\frac{169}{300} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{5}{12}+p)(\frac{6}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{5}{12}}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{5}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{2}p-\frac{5}{12}b+\frac{5}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =-bp+\frac{1}{2}p-\frac{5}{12}b+\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{8}-p)((-3)-q)& =(\color{red}{-p}+\color{orange}{\frac{-5}{8}}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq+3p+\frac{5}{8}q+\frac{5}{8}.3& \text{Uitwerken } \\ & =pq+3p+\frac{5}{8}q+\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-5}{16}+a)(\frac{-4}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{-5}{16}}).(\color{green}{-p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{5}a+\frac{5}{16}p+\frac{5}{16}.\frac{2}{5}& \text{Uitwerken } \\ & =-ap-\frac{2}{5}a+\frac{5}{16}p+\frac{10}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{2}{5}a+\frac{5}{16}p+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{7}{12}-q)(\frac{-10}{11}-x)& =(\color{red}{-q}+\color{orange}{\frac{7}{12}}).(\color{green}{-x}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{7}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{11}q-\frac{7}{12}x-\frac{7}{12}.\frac{10}{11}& \text{Uitwerken } \\ & =qx+\frac{10}{11}q-\frac{7}{12}x-\frac{70}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{10}{11}q-\frac{7}{12}x-\frac{35}{66} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{9}-b)(\frac{-13}{7}-b)& =(\color{red}{-b}+\color{orange}{\frac{-19}{9}}).(\color{green}{-b}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{7}b+\frac{19}{9}b+\frac{19}{9}.\frac{13}{7}& \text{Uitwerken } \\ & =b^2+(\frac{13}{7}+\frac{19}{9})b+\frac{247}{63} & \text{Neem samen} \\ &=b^2+\frac{250}{63}b+\frac{247}{63} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-16}{8}-a)(\frac{11}{16}+x)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{16}a-2x-2.\frac{11}{16}& \text{Uitwerken } \\ & =-ax-\frac{11}{16}a-2x-\frac{22}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{16}a-2x-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{15}{18}-b)(\frac{-8}{16}+x)& =(\color{red}{-b}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{2}b+\frac{5}{6}x-\frac{5}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =-bx+\frac{1}{2}b+\frac{5}{6}x-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{15}{13}+q)((-14)+b)& =(\color{red}{q}+\color{orange}{\frac{15}{13}}).(\color{green}{b}+\color{blue}{(-14)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-14)} + \color{orange}{(\frac{15}{13})} . \color{green}{(b)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = bq-14q+\frac{15}{13}b-\frac{15}{13}.14& \text{Uitwerken } \\ & =bq-14q+\frac{15}{13}b-\frac{210}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{17}{5}-x)(p-\frac{-8}{6})& =(\color{red}{-x}+\color{orange}{\frac{17}{5}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{17}{5})} . \color{green}{(p)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{3}x+\frac{17}{5}p+\frac{17}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =-px-\frac{4}{3}x+\frac{17}{5}p+\frac{68}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{14}{19})(a+14)& =(\color{red}{b}+\color{orange}{\frac{-14}{19}}).(\color{green}{a}+\color{blue}{14})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(14)} + \color{orange}{(\frac{-14}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = ab+14b-\frac{14}{19}a-\frac{14}{19}.14& \text{Uitwerken } \\ & =ab+14b-\frac{14}{19}a-\frac{196}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)