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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{15}{8})(x-\frac{-17}{17})& =(\color{red}{a}+\color{orange}{\frac{15}{8}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{15}{8})} . \color{green}{(x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{15}{8}x+\frac{15}{8}.1& \text{Uitwerken } \\ & =ax+1a+\frac{15}{8}x+\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-(-6))(a+\frac{-4}{20})& =(\color{red}{b}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{5}b+6a-6.\frac{1}{5}& \text{Uitwerken } \\ & =ab-\frac{1}{5}b+6a-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{3}{2}+p)(\frac{5}{11}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-a}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{11}p-\frac{3}{2}a+\frac{3}{2}.\frac{5}{11}& \text{Uitwerken } \\ & =-ap+\frac{5}{11}p-\frac{3}{2}a+\frac{15}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-6}{19}+q)(b+\frac{7}{9})& =(\color{red}{q}+\color{orange}{\frac{-6}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{9}q-\frac{6}{19}b-\frac{6}{19}.\frac{7}{9}& \text{Uitwerken } \\ & =bq+\frac{7}{9}q-\frac{6}{19}b-\frac{42}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{7}{9}q-\frac{6}{19}b-\frac{14}{57} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{9}{19}+q)(p+\frac{12}{9})& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{9}{19})} . \color{green}{(p)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{3}q+\frac{9}{19}p+\frac{9}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =pq+\frac{4}{3}q+\frac{9}{19}p+\frac{36}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{4}{3}q+\frac{9}{19}p+\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{-3}{11})(\frac{15}{10}+a)& =(\color{red}{x}+\color{orange}{\frac{3}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{3}{11})} . \color{green}{(a)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x+\frac{3}{11}a+\frac{3}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x+\frac{3}{11}a+\frac{9}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{2}+p)(b+\frac{-14}{11})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-14}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{11})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-14}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{14}{11}p-2b+2.\frac{14}{11}& \text{Uitwerken } \\ & =bp-\frac{14}{11}p-2b+\frac{28}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{-12}{11})(\frac{15}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{12}{11}}).(\color{green}{p}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{12}{11})} . \color{green}{(p)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{15}{2}b+\frac{12}{11}p+\frac{12}{11}.\frac{15}{2}& \text{Uitwerken } \\ & =bp+\frac{15}{2}b+\frac{12}{11}p+\frac{180}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{15}{2}b+\frac{12}{11}p+\frac{90}{11} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q+\frac{-5}{20})(q+\frac{-19}{2})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{2}q-\frac{1}{4}q+\frac{1}{4}.\frac{19}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{2})+(\frac{-1}{4}))q+\frac{19}{8} & \text{Neem samen} \\ &=q^2-\frac{39}{4}q+\frac{19}{8} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}((-6)-b)(p-\frac{2}{10})& =(\color{red}{-b}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{5}b-6p+6.\frac{1}{5}& \text{Uitwerken } \\ & =-bp+\frac{1}{5}b-6p+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-11}{11})(a-\frac{11}{18})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{18}x+1a-1.\frac{11}{18}& \text{Uitwerken } \\ & =ax-\frac{11}{18}x+1a-\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-12}{2}-p)(x+\frac{4}{7})& =(\color{red}{-p}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{7}p-6x-6.\frac{4}{7}& \text{Uitwerken } \\ & =-px-\frac{4}{7}p-6x-\frac{24}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)