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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(4+q)(\frac{-11}{14}-p)& =(\color{red}{q}+\color{orange}{4}).(\color{green}{-p}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(4)} . \color{green}{(-p)} + \color{orange}{(4)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{14}q-4p-4.\frac{11}{14}& \text{Uitwerken } \\ & =-pq-\frac{11}{14}q-4p-\frac{44}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{11}{14}q-4p-\frac{22}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a+\frac{7}{5})(q-\frac{-11}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{7}{5})} . \color{green}{(q)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{2}a+\frac{7}{5}q+\frac{7}{5}.\frac{11}{2}& \text{Uitwerken } \\ & =aq+\frac{11}{2}a+\frac{7}{5}q+\frac{77}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{19}{15}-q)(a-\frac{-5}{4})& =(\color{red}{-q}+\color{orange}{\frac{19}{15}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{19}{15})} . \color{green}{(a)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{4}q+\frac{19}{15}a+\frac{19}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq-\frac{5}{4}q+\frac{19}{15}a+\frac{95}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{4}q+\frac{19}{15}a+\frac{19}{12} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-11}{2}+a)(b+\frac{11}{15})& =(\color{red}{a}+\color{orange}{\frac{-11}{2}}).(\color{green}{b}+\color{blue}{\frac{11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{15})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{11}{15})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{15}a-\frac{11}{2}b-\frac{11}{2}.\frac{11}{15}& \text{Uitwerken } \\ & =ab+\frac{11}{15}a-\frac{11}{2}b-\frac{121}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{17}{11}+x)(\frac{15}{12}-p)& =(\color{red}{x}+\color{orange}{\frac{17}{11}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{17}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{4}x-\frac{17}{11}p+\frac{17}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =-px+\frac{5}{4}x-\frac{17}{11}p+\frac{85}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{4}{20})(p-\frac{-4}{19})& =(\color{red}{x}+\color{orange}{\frac{1}{5}}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{1}{5})} . \color{green}{(p)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{19}x+\frac{1}{5}p+\frac{1}{5}.\frac{4}{19}& \text{Uitwerken } \\ & =px+\frac{4}{19}x+\frac{1}{5}p+\frac{4}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{9}{5}+a)(\frac{8}{6}+b)& =(\color{red}{a}+\color{orange}{\frac{9}{5}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{9}{5})} . \color{green}{(b)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{3}a+\frac{9}{5}b+\frac{9}{5}.\frac{4}{3}& \text{Uitwerken } \\ & =ab+\frac{4}{3}a+\frac{9}{5}b+\frac{36}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{3}a+\frac{9}{5}b+\frac{12}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{7}{8}+p)(a-\frac{-15}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3p+\frac{7}{8}a+\frac{7}{8}.3& \text{Uitwerken } \\ & =ap+3p+\frac{7}{8}a+\frac{21}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{17}{4})(\frac{12}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-17}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p-\frac{17}{4}b-\frac{17}{4}.1& \text{Uitwerken } \\ & =bp+1p-\frac{17}{4}b-\frac{17}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(3+x)(\frac{-9}{4}-b)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{4}x-3b-3.\frac{9}{4}& \text{Uitwerken } \\ & =-bx-\frac{9}{4}x-3b-\frac{27}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{3}{4}+x)(\frac{11}{16}+q)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{16}x+\frac{3}{4}q+\frac{3}{4}.\frac{11}{16}& \text{Uitwerken } \\ & =qx+\frac{11}{16}x+\frac{3}{4}q+\frac{33}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-18}{19})(\frac{4}{13}-a)& =(\color{red}{p}+\color{orange}{\frac{-18}{19}}).(\color{green}{-a}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{13}p+\frac{18}{19}a-\frac{18}{19}.\frac{4}{13}& \text{Uitwerken } \\ & =-ap+\frac{4}{13}p+\frac{18}{19}a-\frac{72}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)