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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{4}{4}-x)(\frac{-18}{19}-p)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{19}x-1p-1.\frac{18}{19}& \text{Uitwerken } \\ & =px+\frac{18}{19}x-1p-\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{1}{17})(x-\frac{-5}{16})& =(\color{red}{a}+\color{orange}{\frac{-1}{17}}).(\color{green}{x}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{16}a-\frac{1}{17}x-\frac{1}{17}.\frac{5}{16}& \text{Uitwerken } \\ & =ax+\frac{5}{16}a-\frac{1}{17}x-\frac{5}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{15}{8})(p-\frac{-2}{14})& =(\color{red}{b}+\color{orange}{\frac{-15}{8}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{7}b-\frac{15}{8}p-\frac{15}{8}.\frac{1}{7}& \text{Uitwerken } \\ & =bp+\frac{1}{7}b-\frac{15}{8}p-\frac{15}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{7}{10})(\frac{-3}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{5}x-\frac{7}{10}p+\frac{7}{10}.\frac{1}{5}& \text{Uitwerken } \\ & =px-\frac{1}{5}x-\frac{7}{10}p+\frac{7}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{9}{13})(b-\frac{4}{16})& =(\color{red}{x}+\color{orange}{\frac{9}{13}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{9}{13})} . \color{green}{(b)} + \color{orange}{(\frac{9}{13})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{4}x+\frac{9}{13}b-\frac{9}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =bx-\frac{1}{4}x+\frac{9}{13}b-\frac{9}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(17+b)(7+p)& =(\color{red}{b}+\color{orange}{17}).(\color{green}{p}+\color{blue}{7})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(7)} + \color{orange}{(17)} . \color{green}{(p)} + \color{orange}{(17)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = bp+7b+17p+17.7& \text{Uitwerken } \\ & =bp+7b+17p+119 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-15}{17}+x)(\frac{-3}{7}-x)& =(\color{red}{x}+\color{orange}{\frac{-15}{17}}).(\color{green}{-x}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{7}x+\frac{15}{17}x+\frac{15}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{7})+\frac{15}{17})x+(\frac{-45}{119}) & \text{Neem samen} \\ &=-x^2+\frac{54}{119}x+(\frac{-45}{119}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p-\frac{-10}{3})((-18)-p)& =(\color{red}{p}+\color{orange}{\frac{10}{3}}).(\color{green}{-p}+\color{blue}{(-18)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-18)} + \color{orange}{(\frac{10}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -pp-18p-\frac{10}{3}p-\frac{10}{3}.18& \text{Uitwerken } \\ & =-p^2+((-18)+(\frac{-10}{3}))p-\frac{180}{3} & \text{Neem samen} \\ &=-p^2-\frac{64}{3}p-\frac{180}{3} & \text{Maak de som} \\ &=-p^2-\frac{64}{3}p-60 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(a-\frac{-15}{6})(p+\frac{-8}{19})& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{8}{19}a+\frac{5}{2}p-\frac{5}{2}.\frac{8}{19}& \text{Uitwerken } \\ & =ap-\frac{8}{19}a+\frac{5}{2}p-\frac{40}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{8}{19}a+\frac{5}{2}p-\frac{20}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{18}{15})(\frac{-5}{14}-p)& =(\color{red}{a}+\color{orange}{\frac{-6}{5}}).(\color{green}{-p}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{14}a+\frac{6}{5}p+\frac{6}{5}.\frac{5}{14}& \text{Uitwerken } \\ & =-ap-\frac{5}{14}a+\frac{6}{5}p+\frac{30}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{14}a+\frac{6}{5}p+\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{14}{11})(\frac{-13}{17}+q)& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{q}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{17}q-\frac{14}{11}q+\frac{14}{11}.\frac{13}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{17})+(\frac{-14}{11}))q+\frac{182}{187} & \text{Neem samen} \\ &=q^2-\frac{381}{187}q+\frac{182}{187} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q-\frac{-13}{20})(b-\frac{-13}{7})& =(\color{red}{q}+\color{orange}{\frac{13}{20}}).(\color{green}{b}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{7}q+\frac{13}{20}b+\frac{13}{20}.\frac{13}{7}& \text{Uitwerken } \\ & =bq+\frac{13}{7}q+\frac{13}{20}b+\frac{169}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)