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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-12}{18})(x+\frac{5}{13})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{13}b-\frac{2}{3}x-\frac{2}{3}.\frac{5}{13}& \text{Uitwerken } \\ & =bx+\frac{5}{13}b-\frac{2}{3}x-\frac{10}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-6}{4}+q)(\frac{-16}{14}-x)& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{7}q+\frac{3}{2}x+\frac{3}{2}.\frac{8}{7}& \text{Uitwerken } \\ & =-qx-\frac{8}{7}q+\frac{3}{2}x+\frac{24}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{8}{7}q+\frac{3}{2}x+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q+\frac{-1}{15})(\frac{-10}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{-1}{15}}).(\color{green}{-p}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-1}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pq-5q+\frac{1}{15}p+\frac{1}{15}.5& \text{Uitwerken } \\ & =-pq-5q+\frac{1}{15}p+\frac{5}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-5q+\frac{1}{15}p+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{9}+p)(x-\frac{12}{9})& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{3}p-\frac{5}{9}x+\frac{5}{9}.\frac{4}{3}& \text{Uitwerken } \\ & =px-\frac{4}{3}p-\frac{5}{9}x+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{14}+p)(q+\frac{9}{2})& =(\color{red}{p}+\color{orange}{\frac{-1}{14}}).(\color{green}{q}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{2}p-\frac{1}{14}q-\frac{1}{14}.\frac{9}{2}& \text{Uitwerken } \\ & =pq+\frac{9}{2}p-\frac{1}{14}q-\frac{9}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-5}{5})(p-\frac{-17}{14})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{14}x-1p-1.\frac{17}{14}& \text{Uitwerken } \\ & =px+\frac{17}{14}x-1p-\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-20}{5}-p)(a+\frac{-8}{5})& =(\color{red}{-p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{5}p-4a+4.\frac{8}{5}& \text{Uitwerken } \\ & =-ap+\frac{8}{5}p-4a+\frac{32}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-18}{9})(\frac{-1}{12}+q)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{12}a+2q-2.\frac{1}{12}& \text{Uitwerken } \\ & =aq-\frac{1}{12}a+2q-\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{12}a+2q-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{8}{20}-x)(b+\frac{-15}{19})& =(\color{red}{-x}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{19}x+\frac{2}{5}b-\frac{2}{5}.\frac{15}{19}& \text{Uitwerken } \\ & =-bx+\frac{15}{19}x+\frac{2}{5}b-\frac{30}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{15}{19}x+\frac{2}{5}b-\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{-20}{5})(\frac{7}{14}+b)& =(\color{red}{p}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}p+4b+4.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}p+4b+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{2}p+4b+2 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p-\frac{16}{19})(\frac{6}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{-16}{19}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{2}p-\frac{16}{19}p-\frac{16}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+(\frac{1}{2}+(\frac{-16}{19}))p-(\frac{-16}{38}) & \text{Neem samen} \\ &=p^2-\frac{13}{38}p-(\frac{-16}{38}) & \text{Maak de som} \\ &=p^2-\frac{13}{38}p+\frac{8}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(\frac{2}{16}+x)(a+\frac{7}{2})& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{2}x+\frac{1}{8}a+\frac{1}{8}.\frac{7}{2}& \text{Uitwerken } \\ & =ax+\frac{7}{2}x+\frac{1}{8}a+\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)