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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-12}{8}-x)(p+\frac{-19}{14})& =(\color{red}{-x}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{14}x-\frac{3}{2}p+\frac{3}{2}.\frac{19}{14}& \text{Uitwerken } \\ & =-px+\frac{19}{14}x-\frac{3}{2}p+\frac{57}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{7}{6})(\frac{12}{7}+p)& =(\color{red}{x}+\color{orange}{\frac{7}{6}}).(\color{green}{p}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{12}{7}x+\frac{7}{6}p+\frac{7}{6}.\frac{12}{7}& \text{Uitwerken } \\ & =px+\frac{12}{7}x+\frac{7}{6}p+\frac{84}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{12}{7}x+\frac{7}{6}p+2 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-15}{4}-x)(q-\frac{5}{5})& =(\color{red}{-x}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x-\frac{15}{4}q+\frac{15}{4}.1& \text{Uitwerken } \\ & =-qx+1x-\frac{15}{4}q+\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{-2}{7})(x+(-5))& =(\color{red}{q}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5q-\frac{2}{7}x+\frac{2}{7}.5& \text{Uitwerken } \\ & =qx-5q-\frac{2}{7}x+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{-20}{3})(\frac{6}{8}-p)& =(\color{red}{p}+\color{orange}{\frac{20}{3}}).(\color{green}{-p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{20}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{3}{4}p-\frac{20}{3}p+\frac{20}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =-p^2+(\frac{3}{4}+(\frac{-20}{3}))p+(\frac{-60}{12}) & \text{Neem samen} \\ &=-p^2-\frac{71}{12}p+(\frac{-60}{12}) & \text{Maak de som} \\ &=-p^2-\frac{71}{12}p+(-5) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(p-\frac{17}{6})(\frac{2}{6}+p)& =(\color{red}{p}+\color{orange}{\frac{-17}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{3}p-\frac{17}{6}p-\frac{17}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =p^2+(\frac{1}{3}+(\frac{-17}{6}))p-(\frac{-17}{18}) & \text{Neem samen} \\ &=p^2-\frac{15}{6}p-(\frac{-17}{18}) & \text{Maak de som} \\ &=p^2-\frac{5}{2}p+\frac{17}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(\frac{10}{15}-x)(\frac{-5}{6}+p)& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{6}x+\frac{2}{3}p-\frac{2}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =-px+\frac{5}{6}x+\frac{2}{3}p-\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{6}x+\frac{2}{3}p-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-17}{16}-a)(x-\frac{19}{2})& =(\color{red}{-a}+\color{orange}{\frac{-17}{16}}).(\color{green}{x}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{2}a-\frac{17}{16}x+\frac{17}{16}.\frac{19}{2}& \text{Uitwerken } \\ & =-ax+\frac{19}{2}a-\frac{17}{16}x+\frac{323}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{19}{8}+b)(\frac{-15}{16}+b)& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{16}b+\frac{19}{8}b-\frac{19}{8}.\frac{15}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{16})+\frac{19}{8})b-(\frac{-285}{128}) & \text{Neem samen} \\ &=b^2+\frac{23}{16}b-(\frac{-285}{128}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{19}{4}-a)(p-\frac{13}{2})& =(\color{red}{-a}+\color{orange}{\frac{19}{4}}).(\color{green}{p}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{19}{4})} . \color{green}{(p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{2}a+\frac{19}{4}p-\frac{19}{4}.\frac{13}{2}& \text{Uitwerken } \\ & =-ap+\frac{13}{2}a+\frac{19}{4}p-\frac{247}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{2}{3}+a)(\frac{-19}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{9}a+\frac{2}{3}p-\frac{2}{3}.\frac{19}{9}& \text{Uitwerken } \\ & =ap-\frac{19}{9}a+\frac{2}{3}p-\frac{38}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-20}{11})(\frac{-8}{8}-a)& =(\color{red}{p}+\color{orange}{\frac{-20}{11}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1p+\frac{20}{11}a+\frac{20}{11}.1& \text{Uitwerken } \\ & =-ap-1p+\frac{20}{11}a+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)