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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{14}{15})(\frac{12}{7}-a)& =(\color{red}{p}+\color{orange}{\frac{14}{15}}).(\color{green}{-a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{12}{7}p-\frac{14}{15}a+\frac{14}{15}.\frac{12}{7}& \text{Uitwerken } \\ & =-ap+\frac{12}{7}p-\frac{14}{15}a+\frac{168}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{12}{7}p-\frac{14}{15}a+\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x+\frac{5}{15})(p-\frac{-13}{2})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{2}x+\frac{1}{3}p+\frac{1}{3}.\frac{13}{2}& \text{Uitwerken } \\ & =px+\frac{13}{2}x+\frac{1}{3}p+\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{5}+p)(p-\frac{5}{13})& =(\color{red}{p}+\color{orange}{\frac{-19}{5}}).(\color{green}{p}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{13}p-\frac{19}{5}p+\frac{19}{5}.\frac{5}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{13})+(\frac{-19}{5}))p+\frac{95}{65} & \text{Neem samen} \\ &=p^2-\frac{272}{65}p+\frac{95}{65} & \text{Maak de som} \\ &=p^2-\frac{272}{65}p+\frac{19}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(x+\frac{2}{19})(b-\frac{-17}{5})& =(\color{red}{x}+\color{orange}{\frac{2}{19}}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{2}{19})} . \color{green}{(b)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{5}x+\frac{2}{19}b+\frac{2}{19}.\frac{17}{5}& \text{Uitwerken } \\ & =bx+\frac{17}{5}x+\frac{2}{19}b+\frac{34}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{-8}{9})(q+\frac{-6}{4})& =(\color{red}{q}+\color{orange}{\frac{-8}{9}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{2}q-\frac{8}{9}q+\frac{8}{9}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{2})+(\frac{-8}{9}))q+\frac{24}{18} & \text{Neem samen} \\ &=q^2-\frac{43}{18}q+\frac{24}{18} & \text{Maak de som} \\ &=q^2-\frac{43}{18}q+\frac{4}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(a+\frac{-15}{6})(b+\frac{9}{6})& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{2}a-\frac{5}{2}b-\frac{5}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ab+\frac{3}{2}a-\frac{5}{2}b-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-8}{18})(a+\frac{6}{14})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{7}a+\frac{4}{9}a+\frac{4}{9}.\frac{3}{7}& \text{Uitwerken } \\ & =a^2+(\frac{3}{7}+\frac{4}{9})a+\frac{12}{63} & \text{Neem samen} \\ &=a^2+\frac{55}{63}a+\frac{12}{63} & \text{Maak de som} \\ &=a^2+\frac{55}{63}a+\frac{4}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(b-\frac{-5}{17})(b-\frac{4}{11})& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{b}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{4}{11}b+\frac{5}{17}b-\frac{5}{17}.\frac{4}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-4}{11})+\frac{5}{17})b-(\frac{-20}{187}) & \text{Neem samen} \\ &=b^2-\frac{13}{187}b-(\frac{-20}{187}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(a+\frac{8}{17})(p+\frac{16}{15})& =(\color{red}{a}+\color{orange}{\frac{8}{17}}).(\color{green}{p}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{15}a+\frac{8}{17}p+\frac{8}{17}.\frac{16}{15}& \text{Uitwerken } \\ & =ap+\frac{16}{15}a+\frac{8}{17}p+\frac{128}{255} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-7}{8})(a-\frac{17}{3})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{a}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{3}x-\frac{7}{8}a+\frac{7}{8}.\frac{17}{3}& \text{Uitwerken } \\ & =ax-\frac{17}{3}x-\frac{7}{8}a+\frac{119}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-2}{7}-b)(\frac{-10}{14}-a)& =(\color{red}{-b}+\color{orange}{\frac{-2}{7}}).(\color{green}{-a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{7}b+\frac{2}{7}a+\frac{2}{7}.\frac{5}{7}& \text{Uitwerken } \\ & =ab+\frac{5}{7}b+\frac{2}{7}a+\frac{10}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{-13}{13})(a-\frac{8}{11})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{11}p+1a-1.\frac{8}{11}& \text{Uitwerken } \\ & =ap-\frac{8}{11}p+1a-\frac{8}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)