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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{20}{5})(p-\frac{-18}{11})& =(\color{red}{x}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{11}x+4p+4.\frac{18}{11}& \text{Uitwerken } \\ & =px+\frac{18}{11}x+4p+\frac{72}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-4)(\frac{-20}{4}+b)& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-5)} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bx-5x-4b+4.5& \text{Uitwerken } \\ & =bx-5x-4b+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{6}{6}-q)(\frac{-5}{15}+p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{3}q+1p-1.\frac{1}{3}& \text{Uitwerken } \\ & =-pq+\frac{1}{3}q+1p-\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-16}{8})(p+\frac{-19}{18})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{18}q+2p-2.\frac{19}{18}& \text{Uitwerken } \\ & =pq-\frac{19}{18}q+2p-\frac{38}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{18}q+2p-\frac{19}{9} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-10}{16})(a-\frac{-10}{17})& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{a}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{17}p+\frac{5}{8}a+\frac{5}{8}.\frac{10}{17}& \text{Uitwerken } \\ & =ap+\frac{10}{17}p+\frac{5}{8}a+\frac{50}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{10}{17}p+\frac{5}{8}a+\frac{25}{68} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{12}{12}+x)(\frac{-16}{17}-b)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{17}x-1b-1.\frac{16}{17}& \text{Uitwerken } \\ & =-bx-\frac{16}{17}x-1b-\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{-5}{16})(x-\frac{4}{10})& =(\color{red}{b}+\color{orange}{\frac{-5}{16}}).(\color{green}{x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{5}b-\frac{5}{16}x+\frac{5}{16}.\frac{2}{5}& \text{Uitwerken } \\ & =bx-\frac{2}{5}b-\frac{5}{16}x+\frac{10}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{2}{5}b-\frac{5}{16}x+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+2)(x+\frac{13}{20})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{20}p+2x+2.\frac{13}{20}& \text{Uitwerken } \\ & =px+\frac{13}{20}p+2x+\frac{26}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{13}{20}p+2x+\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(x+\frac{8}{4})(\frac{1}{10}+p)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{10}x+2p+2.\frac{1}{10}& \text{Uitwerken } \\ & =px+\frac{1}{10}x+2p+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{10}x+2p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a+\frac{1}{8})(a+\frac{-18}{15})& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{6}{5}a+\frac{1}{8}a-\frac{1}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-6}{5})+\frac{1}{8})a-(\frac{-6}{40}) & \text{Neem samen} \\ &=a^2-\frac{43}{40}a-(\frac{-6}{40}) & \text{Maak de som} \\ &=a^2-\frac{43}{40}a+\frac{3}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
11. \(\begin{align}(\frac{-12}{16}+b)(\frac{-3}{8}+b)& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{8}b-\frac{3}{4}b+\frac{3}{4}.\frac{3}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{8})+(\frac{-3}{4}))b+\frac{9}{32} & \text{Neem samen} \\ &=b^2-\frac{9}{8}b+\frac{9}{32} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{11}-p)(\frac{-17}{12}-p)& =(\color{red}{-p}+\color{orange}{\frac{-1}{11}}).(\color{green}{-p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{17}{12}p+\frac{1}{11}p+\frac{1}{11}.\frac{17}{12}& \text{Uitwerken } \\ & =p^2+(\frac{17}{12}+\frac{1}{11})p+\frac{17}{132} & \text{Neem samen} \\ &=p^2+\frac{199}{132}p+\frac{17}{132} & \text{Maak de som} \\\end{align}\)