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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{13}{3})(a+\frac{6}{8})& =(\color{red}{p}+\color{orange}{\frac{-13}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}p-\frac{13}{3}a-\frac{13}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}p-\frac{13}{3}a-\frac{39}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}p-\frac{13}{3}a-\frac{13}{4} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{14}{3}+b)(q+\frac{10}{18})& =(\color{red}{b}+\color{orange}{\frac{14}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{14}{3})} . \color{green}{(q)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{9}b+\frac{14}{3}q+\frac{14}{3}.\frac{5}{9}& \text{Uitwerken } \\ & =bq+\frac{5}{9}b+\frac{14}{3}q+\frac{70}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{3}{8}-q)(a+\frac{-19}{16})& =(\color{red}{-q}+\color{orange}{\frac{3}{8}}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{16}q+\frac{3}{8}a-\frac{3}{8}.\frac{19}{16}& \text{Uitwerken } \\ & =-aq+\frac{19}{16}q+\frac{3}{8}a-\frac{57}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(7-a)(x-\frac{2}{9})& =(\color{red}{-a}+\color{orange}{7}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(7)} . \color{green}{(x)} + \color{orange}{(7)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{9}a+7x-7.\frac{2}{9}& \text{Uitwerken } \\ & =-ax+\frac{2}{9}a+7x-\frac{14}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a+\frac{-3}{6})(b+\frac{3}{3})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a-\frac{1}{2}b-\frac{1}{2}.1& \text{Uitwerken } \\ & =ab+1a-\frac{1}{2}b-\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(4-a)(\frac{9}{5}+a)& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(4)} . \color{green}{(a)} + \color{orange}{(4)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{5}a+4a+4.\frac{9}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{5})+4)a+(\frac{-36}{5}) & \text{Neem samen} \\ &=-a^2+\frac{11}{5}a+(\frac{-36}{5}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(p+\frac{3}{14})(\frac{-12}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{3}{14}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{3}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp-2p-\frac{3}{14}p-\frac{3}{14}.2& \text{Uitwerken } \\ & =-p^2+((-2)+(\frac{-3}{14}))p-\frac{6}{14} & \text{Neem samen} \\ &=-p^2-\frac{31}{14}p-\frac{6}{14} & \text{Maak de som} \\ &=-p^2-\frac{31}{14}p-\frac{3}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(b+\frac{11}{16})(p+\frac{-10}{20})& =(\color{red}{b}+\color{orange}{\frac{11}{16}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}b+\frac{11}{16}p-\frac{11}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}b+\frac{11}{16}p-\frac{11}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-19}{15})(\frac{-13}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{19}{15}}).(\color{green}{-b}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{15}p-\frac{19}{15}b-\frac{19}{15}.\frac{13}{15}& \text{Uitwerken } \\ & =-bp-\frac{13}{15}p-\frac{19}{15}b-\frac{247}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{13}{17}-x)(\frac{-20}{6}+p)& =(\color{red}{-x}+\color{orange}{\frac{13}{17}}).(\color{green}{p}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{13}{17})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{3}x+\frac{13}{17}p-\frac{13}{17}.\frac{10}{3}& \text{Uitwerken } \\ & =-px+\frac{10}{3}x+\frac{13}{17}p-\frac{130}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{14}{17}-q)(b+\frac{3}{13})& =(\color{red}{-q}+\color{orange}{\frac{14}{17}}).(\color{green}{b}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{13}q+\frac{14}{17}b+\frac{14}{17}.\frac{3}{13}& \text{Uitwerken } \\ & =-bq-\frac{3}{13}q+\frac{14}{17}b+\frac{42}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-2}{13})(\frac{4}{13}-x)& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{-x}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{13}p+\frac{2}{13}x-\frac{2}{13}.\frac{4}{13}& \text{Uitwerken } \\ & =-px+\frac{4}{13}p+\frac{2}{13}x-\frac{8}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)