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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{20}{13})(a+\frac{14}{9})& =(\color{red}{q}+\color{orange}{\frac{-20}{13}}).(\color{green}{a}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{9}q-\frac{20}{13}a-\frac{20}{13}.\frac{14}{9}& \text{Uitwerken } \\ & =aq+\frac{14}{9}q-\frac{20}{13}a-\frac{280}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{5}{5}-x)(\frac{3}{13}-b)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{13}x-1b+1.\frac{3}{13}& \text{Uitwerken } \\ & =bx-\frac{3}{13}x-1b+\frac{3}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-17}{16}-a)(a+\frac{12}{6})& =(\color{red}{-a}+\color{orange}{\frac{-17}{16}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -aa-2a-\frac{17}{16}a-\frac{17}{16}.2& \text{Uitwerken } \\ & =-a^2+((-2)+(\frac{-17}{16}))a-\frac{34}{16} & \text{Neem samen} \\ &=-a^2-\frac{49}{16}a-\frac{34}{16} & \text{Maak de som} \\ &=-a^2-\frac{49}{16}a-\frac{17}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(x-\frac{-13}{7})(p+\frac{3}{20})& =(\color{red}{x}+\color{orange}{\frac{13}{7}}).(\color{green}{p}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{20}x+\frac{13}{7}p+\frac{13}{7}.\frac{3}{20}& \text{Uitwerken } \\ & =px+\frac{3}{20}x+\frac{13}{7}p+\frac{39}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-19}{18}+p)(b-\frac{6}{14})& =(\color{red}{p}+\color{orange}{\frac{-19}{18}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{7}p-\frac{19}{18}b+\frac{19}{18}.\frac{3}{7}& \text{Uitwerken } \\ & =bp-\frac{3}{7}p-\frac{19}{18}b+\frac{57}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{7}p-\frac{19}{18}b+\frac{19}{42} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{6}-b)(\frac{-14}{17}-a)& =(\color{red}{-b}+\color{orange}{\frac{-17}{6}}).(\color{green}{-a}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{14}{17}b+\frac{17}{6}a+\frac{17}{6}.\frac{14}{17}& \text{Uitwerken } \\ & =ab+\frac{14}{17}b+\frac{17}{6}a+\frac{238}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{14}{17}b+\frac{17}{6}a+\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a-\frac{-19}{14})(p+\frac{10}{11})& =(\color{red}{a}+\color{orange}{\frac{19}{14}}).(\color{green}{p}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{19}{14})} . \color{green}{(p)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{11}a+\frac{19}{14}p+\frac{19}{14}.\frac{10}{11}& \text{Uitwerken } \\ & =ap+\frac{10}{11}a+\frac{19}{14}p+\frac{190}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{10}{11}a+\frac{19}{14}p+\frac{95}{77} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-5}{8}-b)(p-\frac{-8}{14})& =(\color{red}{-b}+\color{orange}{\frac{-5}{8}}).(\color{green}{p}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{7}b-\frac{5}{8}p-\frac{5}{8}.\frac{4}{7}& \text{Uitwerken } \\ & =-bp-\frac{4}{7}b-\frac{5}{8}p-\frac{20}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{7}b-\frac{5}{8}p-\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{6}{7}+x)(b-\frac{-20}{18})& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{9}x+\frac{6}{7}b+\frac{6}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =bx+\frac{10}{9}x+\frac{6}{7}b+\frac{60}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{10}{9}x+\frac{6}{7}b+\frac{20}{21} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{16}-p)(b+\frac{-4}{6})& =(\color{red}{-p}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{2}{3}p-\frac{1}{4}b+\frac{1}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp+\frac{2}{3}p-\frac{1}{4}b+\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{2}{3}p-\frac{1}{4}b+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{11}{14})(\frac{-5}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{-11}{14}}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{9}q-\frac{11}{14}a+\frac{11}{14}.\frac{5}{9}& \text{Uitwerken } \\ & =aq-\frac{5}{9}q-\frac{11}{14}a+\frac{55}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{18}{19}+p)(p-\frac{9}{3})& =(\color{red}{p}+\color{orange}{\frac{18}{19}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pp-3p+\frac{18}{19}p-\frac{18}{19}.3& \text{Uitwerken } \\ & =p^2+((-3)+\frac{18}{19})p-(\frac{-54}{19}) & \text{Neem samen} \\ &=p^2-\frac{39}{19}p-(\frac{-54}{19}) & \text{Maak de som} \\\end{align}\)