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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-20}{7}+p)(\frac{8}{12}-p)& =(\color{red}{p}+\color{orange}{\frac{-20}{7}}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{2}{3}p+\frac{20}{7}p-\frac{20}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{2}{3}+\frac{20}{7})p-\frac{40}{21} & \text{Neem samen} \\ &=-p^2+\frac{74}{21}p-\frac{40}{21} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{16}{16}-q)(b-\frac{-5}{13})& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{13}q+1b+1.\frac{5}{13}& \text{Uitwerken } \\ & =-bq-\frac{5}{13}q+1b+\frac{5}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x+\frac{10}{7})(\frac{-13}{7}+x)& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{7}x+\frac{10}{7}x-\frac{10}{7}.\frac{13}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{7})+\frac{10}{7})x-(\frac{-130}{49}) & \text{Neem samen} \\ &=x^2-\frac{3}{7}x-(\frac{-130}{49}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b-\frac{-14}{17})(a+\frac{-18}{9})& =(\color{red}{b}+\color{orange}{\frac{14}{17}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{14}{17})} . \color{green}{(a)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2b+\frac{14}{17}a-\frac{14}{17}.2& \text{Uitwerken } \\ & =ab-2b+\frac{14}{17}a-\frac{28}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{6}{17})(a+\frac{-8}{12})& =(\color{red}{x}+\color{orange}{\frac{6}{17}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{6}{17})} . \color{green}{(a)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{3}x+\frac{6}{17}a-\frac{6}{17}.\frac{2}{3}& \text{Uitwerken } \\ & =ax-\frac{2}{3}x+\frac{6}{17}a-\frac{12}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{3}x+\frac{6}{17}a-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-13}{2}+x)(\frac{-14}{3}-p)& =(\color{red}{x}+\color{orange}{\frac{-13}{2}}).(\color{green}{-p}+\color{blue}{\frac{-14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{3})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{-14}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{14}{3}x+\frac{13}{2}p+\frac{13}{2}.\frac{14}{3}& \text{Uitwerken } \\ & =-px-\frac{14}{3}x+\frac{13}{2}p+\frac{182}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{14}{3}x+\frac{13}{2}p+\frac{91}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{-11}{8})(\frac{-3}{15}-a)& =(\color{red}{q}+\color{orange}{\frac{-11}{8}}).(\color{green}{-a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{5}q+\frac{11}{8}a+\frac{11}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =-aq-\frac{1}{5}q+\frac{11}{8}a+\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{1}{19})(\frac{10}{14}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{19}}).(\color{green}{q}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{1}{19})} . \color{green}{(q)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{7}b+\frac{1}{19}q+\frac{1}{19}.\frac{5}{7}& \text{Uitwerken } \\ & =bq+\frac{5}{7}b+\frac{1}{19}q+\frac{5}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{5}-x)(\frac{18}{4}-b)& =(\color{red}{-x}+\color{orange}{\frac{7}{5}}).(\color{green}{-b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{2}x-\frac{7}{5}b+\frac{7}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =bx-\frac{9}{2}x-\frac{7}{5}b+\frac{63}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{5}{14}+p)(\frac{-9}{8}+b)& =(\color{red}{p}+\color{orange}{\frac{5}{14}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{5}{14})} . \color{green}{(b)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{8}p+\frac{5}{14}b-\frac{5}{14}.\frac{9}{8}& \text{Uitwerken } \\ & =bp-\frac{9}{8}p+\frac{5}{14}b-\frac{45}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-(-3))(\frac{8}{4}-p)& =(\color{red}{a}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2a-3p+3.2& \text{Uitwerken } \\ & =-ap+2a-3p+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{6}{18}-a)(\frac{15}{7}-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{3}}).(\color{green}{-x}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{7}a-\frac{1}{3}x+\frac{1}{3}.\frac{15}{7}& \text{Uitwerken } \\ & =ax-\frac{15}{7}a-\frac{1}{3}x+\frac{15}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{15}{7}a-\frac{1}{3}x+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)