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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-1}{2}-p)(x+\frac{-15}{14})& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{15}{14}p-\frac{1}{2}x+\frac{1}{2}.\frac{15}{14}& \text{Uitwerken } \\ & =-px+\frac{15}{14}p-\frac{1}{2}x+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{6}{12})(\frac{-14}{12}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{6}b-\frac{1}{2}q+\frac{1}{2}.\frac{7}{6}& \text{Uitwerken } \\ & =bq-\frac{7}{6}b-\frac{1}{2}q+\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{2}{15})(\frac{14}{20}+x)& =(\color{red}{x}+\color{orange}{\frac{2}{15}}).(\color{green}{x}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{7}{10}x+\frac{2}{15}x+\frac{2}{15}.\frac{7}{10}& \text{Uitwerken } \\ & =x^2+(\frac{7}{10}+\frac{2}{15})x+\frac{14}{150} & \text{Neem samen} \\ &=x^2+\frac{25}{30}x+\frac{14}{150} & \text{Maak de som} \\ &=x^2+\frac{5}{6}x+\frac{7}{75} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(b+\frac{1}{4})(\frac{16}{10}-a)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{-a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{5}b-\frac{1}{4}a+\frac{1}{4}.\frac{8}{5}& \text{Uitwerken } \\ & =-ab+\frac{8}{5}b-\frac{1}{4}a+\frac{8}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{8}{5}b-\frac{1}{4}a+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{18}-p)(\frac{4}{11}-b)& =(\color{red}{-p}+\color{orange}{\frac{-2}{9}}).(\color{green}{-b}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{11}p+\frac{2}{9}b-\frac{2}{9}.\frac{4}{11}& \text{Uitwerken } \\ & =bp-\frac{4}{11}p+\frac{2}{9}b-\frac{8}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{-17}{16})(b+\frac{-20}{5})& =(\color{red}{x}+\color{orange}{\frac{17}{16}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{17}{16})} . \color{green}{(b)} + \color{orange}{(\frac{17}{16})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bx-4x+\frac{17}{16}b-\frac{17}{16}.4& \text{Uitwerken } \\ & =bx-4x+\frac{17}{16}b-\frac{68}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-4x+\frac{17}{16}b-\frac{17}{4} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{7}+x)(x-\frac{-8}{8})& =(\color{red}{x}+\color{orange}{\frac{-11}{7}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = xx+1x-\frac{11}{7}x-\frac{11}{7}.1& \text{Uitwerken } \\ & =x^2+(1+(\frac{-11}{7}))x-(\frac{-11}{7}) & \text{Neem samen} \\ &=x^2-\frac{4}{7}x-(\frac{-11}{7}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{-12}{2}-b)(p-\frac{-3}{19})& =(\color{red}{-b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{19}b-6p-6.\frac{3}{19}& \text{Uitwerken } \\ & =-bp-\frac{3}{19}b-6p-\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{16}+b)(p-\frac{-6}{14})& =(\color{red}{b}+\color{orange}{\frac{-13}{16}}).(\color{green}{p}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{7}b-\frac{13}{16}p-\frac{13}{16}.\frac{3}{7}& \text{Uitwerken } \\ & =bp+\frac{3}{7}b-\frac{13}{16}p-\frac{39}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{10}-p)(a+\frac{6}{18})& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{3}p-1a-1.\frac{1}{3}& \text{Uitwerken } \\ & =-ap-\frac{1}{3}p-1a-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{13}{17}+p)(\frac{-12}{17}+p)& =(\color{red}{p}+\color{orange}{\frac{13}{17}}).(\color{green}{p}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{12}{17}p+\frac{13}{17}p-\frac{13}{17}.\frac{12}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-12}{17})+\frac{13}{17})p-(\frac{-156}{289}) & \text{Neem samen} \\ &=p^2+\frac{1}{17}p-(\frac{-156}{289}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-6}{20}+x)(\frac{4}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{11}x-\frac{3}{10}a-\frac{3}{10}.\frac{4}{11}& \text{Uitwerken } \\ & =ax+\frac{4}{11}x-\frac{3}{10}a-\frac{12}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{4}{11}x-\frac{3}{10}a-\frac{6}{55} & \text{Vereenvoudig} \\\end{align}\)