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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-17}{12})(p-\frac{-1}{2})& =(\color{red}{b}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}b-\frac{17}{12}p-\frac{17}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}b-\frac{17}{12}p-\frac{17}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{-3}{18})(x+\frac{2}{7})& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{7}x-\frac{1}{6}x-\frac{1}{6}.\frac{2}{7}& \text{Uitwerken } \\ & =x^2+(\frac{2}{7}+(\frac{-1}{6}))x-(\frac{-2}{42}) & \text{Neem samen} \\ &=x^2+\frac{5}{42}x-(\frac{-2}{42}) & \text{Maak de som} \\ &=x^2+\frac{5}{42}x+\frac{1}{21} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{11}+a)(p+\frac{10}{8})& =(\color{red}{a}+\color{orange}{\frac{-13}{11}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{4}a-\frac{13}{11}p-\frac{13}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =ap+\frac{5}{4}a-\frac{13}{11}p-\frac{65}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{9}{2})(\frac{2}{20}+b)& =(\color{red}{b}+\color{orange}{\frac{-9}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{10}b-\frac{9}{2}b-\frac{9}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =b^2+(\frac{1}{10}+(\frac{-9}{2}))b-(\frac{-9}{20}) & \text{Neem samen} \\ &=b^2-\frac{44}{10}b-(\frac{-9}{20}) & \text{Maak de som} \\ &=b^2-\frac{22}{5}b+\frac{9}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(\frac{9}{19}-p)(\frac{-13}{19}+b)& =(\color{red}{-p}+\color{orange}{\frac{9}{19}}).(\color{green}{b}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{19}p+\frac{9}{19}b-\frac{9}{19}.\frac{13}{19}& \text{Uitwerken } \\ & =-bp+\frac{13}{19}p+\frac{9}{19}b-\frac{117}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{17}{20})(\frac{-9}{13}-q)& =(\color{red}{a}+\color{orange}{\frac{-17}{20}}).(\color{green}{-q}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{9}{13}a+\frac{17}{20}q+\frac{17}{20}.\frac{9}{13}& \text{Uitwerken } \\ & =-aq-\frac{9}{13}a+\frac{17}{20}q+\frac{153}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{2}{4})(x+\frac{-14}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{5}q+\frac{1}{2}x-\frac{1}{2}.\frac{7}{5}& \text{Uitwerken } \\ & =qx-\frac{7}{5}q+\frac{1}{2}x-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{15}{5})(p+\frac{6}{20})& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{10}x-3p-3.\frac{3}{10}& \text{Uitwerken } \\ & =px+\frac{3}{10}x-3p-\frac{9}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{1}{20}-p)(a-\frac{-9}{10})& =(\color{red}{-p}+\color{orange}{\frac{1}{20}}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{1}{20})} . \color{green}{(a)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{10}p+\frac{1}{20}a+\frac{1}{20}.\frac{9}{10}& \text{Uitwerken } \\ & =-ap-\frac{9}{10}p+\frac{1}{20}a+\frac{9}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{6}{2})(\frac{10}{13}-a)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{10}{13}q-3a+3.\frac{10}{13}& \text{Uitwerken } \\ & =-aq+\frac{10}{13}q-3a+\frac{30}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-8}{2}-a)(p+\frac{-11}{17})& =(\color{red}{-a}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{17}a-4p+4.\frac{11}{17}& \text{Uitwerken } \\ & =-ap+\frac{11}{17}a-4p+\frac{44}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}((-18)-p)(\frac{-7}{16}-x)& =(\color{red}{-p}+\color{orange}{(-18)}).(\color{green}{-x}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(-18)} . \color{green}{(-x)} + \color{orange}{(-18)} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{16}p+18x+18.\frac{7}{16}& \text{Uitwerken } \\ & =px+\frac{7}{16}p+18x+\frac{126}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{16}p+18x+\frac{63}{8} & \text{Vereenvoudig} \\\end{align}\)