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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{10}+p)(x-\frac{5}{9})& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{x}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{19}{10})} . \color{green}{(x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{9}p+\frac{19}{10}x-\frac{19}{10}.\frac{5}{9}& \text{Uitwerken } \\ & =px-\frac{5}{9}p+\frac{19}{10}x-\frac{95}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{9}p+\frac{19}{10}x-\frac{19}{18} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{12}{6}-a)(b-\frac{12}{14})& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{6}{7}a+2b-2.\frac{6}{7}& \text{Uitwerken } \\ & =-ab+\frac{6}{7}a+2b-\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{6}{2})(\frac{-5}{19}+q)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{19}b+3q-3.\frac{5}{19}& \text{Uitwerken } \\ & =bq-\frac{5}{19}b+3q-\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{12}{4})(\frac{1}{5}+p)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{5}x+3p+3.\frac{1}{5}& \text{Uitwerken } \\ & =px+\frac{1}{5}x+3p+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{-11}{9})(x-\frac{8}{13})& =(\color{red}{x}+\color{orange}{\frac{-11}{9}}).(\color{green}{x}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{8}{13}x-\frac{11}{9}x+\frac{11}{9}.\frac{8}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-8}{13})+(\frac{-11}{9}))x+\frac{88}{117} & \text{Neem samen} \\ &=x^2-\frac{215}{117}x+\frac{88}{117} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b-\frac{1}{13})(q+\frac{-15}{6})& =(\color{red}{b}+\color{orange}{\frac{-1}{13}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{2}b-\frac{1}{13}q+\frac{1}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =bq-\frac{5}{2}b-\frac{1}{13}q+\frac{5}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{15}-x)(\frac{5}{4}-a)& =(\color{red}{-x}+\color{orange}{\frac{-4}{15}}).(\color{green}{-a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{4}x+\frac{4}{15}a-\frac{4}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =ax-\frac{5}{4}x+\frac{4}{15}a-\frac{20}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{4}x+\frac{4}{15}a-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{19}-q)(\frac{-2}{4}-q)& =(\color{red}{-q}+\color{orange}{\frac{-9}{19}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q+\frac{9}{19}q+\frac{9}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+\frac{9}{19})q+\frac{9}{38} & \text{Neem samen} \\ &=q^2+\frac{37}{38}q+\frac{9}{38} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(q-\frac{8}{17})(x-\frac{-10}{20})& =(\color{red}{q}+\color{orange}{\frac{-8}{17}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}q-\frac{8}{17}x-\frac{8}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}q-\frac{8}{17}x-\frac{8}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}q-\frac{8}{17}x-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{1}{18}-q)(p+\frac{-1}{11})& =(\color{red}{-q}+\color{orange}{\frac{1}{18}}).(\color{green}{p}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{1}{18})} . \color{green}{(p)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{11}q+\frac{1}{18}p-\frac{1}{18}.\frac{1}{11}& \text{Uitwerken } \\ & =-pq+\frac{1}{11}q+\frac{1}{18}p-\frac{1}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-10}{10})(x+\frac{-15}{4})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{4}a-1x+1.\frac{15}{4}& \text{Uitwerken } \\ & =ax-\frac{15}{4}a-1x+\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{12}-a)(p-\frac{-16}{16})& =(\color{red}{-a}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a-\frac{5}{3}p-\frac{5}{3}.1& \text{Uitwerken } \\ & =-ap-1a-\frac{5}{3}p-\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)