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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{12}{15}+a)(\frac{16}{13}-q)& =(\color{red}{a}+\color{orange}{\frac{4}{5}}).(\color{green}{-q}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{16}{13}a-\frac{4}{5}q+\frac{4}{5}.\frac{16}{13}& \text{Uitwerken } \\ & =-aq+\frac{16}{13}a-\frac{4}{5}q+\frac{64}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{6}{16}-b)(\frac{-18}{3}-x)& =(\color{red}{-b}+\color{orange}{\frac{3}{8}}).(\color{green}{-x}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(-6)} + \color{orange}{(\frac{3}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = bx+6b-\frac{3}{8}x-\frac{3}{8}.6& \text{Uitwerken } \\ & =bx+6b-\frac{3}{8}x-\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+6b-\frac{3}{8}x-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{14}{10})(x-\frac{10}{20})& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}b+\frac{7}{5}x-\frac{7}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}b+\frac{7}{5}x-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-15}{16}-p)(\frac{-7}{18}-b)& =(\color{red}{-p}+\color{orange}{\frac{-15}{16}}).(\color{green}{-b}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{18}p+\frac{15}{16}b+\frac{15}{16}.\frac{7}{18}& \text{Uitwerken } \\ & =bp+\frac{7}{18}p+\frac{15}{16}b+\frac{105}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{18}p+\frac{15}{16}b+\frac{35}{96} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{5}{16}-x)(x-\frac{1}{5})& =(\color{red}{-x}+\color{orange}{\frac{5}{16}}).(\color{green}{x}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{5}x+\frac{5}{16}x-\frac{5}{16}.\frac{1}{5}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{5}+\frac{5}{16})x-\frac{5}{80} & \text{Neem samen} \\ &=-x^2+\frac{41}{80}x-\frac{5}{80} & \text{Maak de som} \\ &=-x^2+\frac{41}{80}x-\frac{1}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(\frac{-13}{18}+x)(b-\frac{11}{12})& =(\color{red}{x}+\color{orange}{\frac{-13}{18}}).(\color{green}{b}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{12}x-\frac{13}{18}b+\frac{13}{18}.\frac{11}{12}& \text{Uitwerken } \\ & =bx-\frac{11}{12}x-\frac{13}{18}b+\frac{143}{216} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{14}+x)(\frac{-12}{16}-x)& =(\color{red}{x}+\color{orange}{\frac{-19}{14}}).(\color{green}{-x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-19}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{14})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{4}x+\frac{19}{14}x+\frac{19}{14}.\frac{3}{4}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{4})+\frac{19}{14})x+(\frac{-57}{56}) & \text{Neem samen} \\ &=-x^2+\frac{17}{28}x+(\frac{-57}{56}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(b+\frac{-16}{14})(\frac{-13}{3}-q)& =(\color{red}{b}+\color{orange}{\frac{-8}{7}}).(\color{green}{-q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{3}b+\frac{8}{7}q+\frac{8}{7}.\frac{13}{3}& \text{Uitwerken } \\ & =-bq-\frac{13}{3}b+\frac{8}{7}q+\frac{104}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{13}{8})(\frac{-15}{9}+q)& =(\color{red}{a}+\color{orange}{\frac{-13}{8}}).(\color{green}{q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{3}a-\frac{13}{8}q+\frac{13}{8}.\frac{5}{3}& \text{Uitwerken } \\ & =aq-\frac{5}{3}a-\frac{13}{8}q+\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{18}{9}+x)(b-\frac{11}{16})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{16}x+2b-2.\frac{11}{16}& \text{Uitwerken } \\ & =bx-\frac{11}{16}x+2b-\frac{22}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{11}{16}x+2b-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{8}+b)(b+\frac{-3}{16})& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{16}b-\frac{3}{8}b+\frac{3}{8}.\frac{3}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{16})+(\frac{-3}{8}))b+\frac{9}{128} & \text{Neem samen} \\ &=b^2-\frac{9}{16}b+\frac{9}{128} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{13}{10}-p)(q+\frac{2}{4})& =(\color{red}{-p}+\color{orange}{\frac{13}{10}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}p+\frac{13}{10}q+\frac{13}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}p+\frac{13}{10}q+\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)