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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{3}{14})(p-\frac{-14}{9})& =(\color{red}{a}+\color{orange}{\frac{-3}{14}}).(\color{green}{p}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-3}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{14})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{9}a-\frac{3}{14}p-\frac{3}{14}.\frac{14}{9}& \text{Uitwerken } \\ & =ap+\frac{14}{9}a-\frac{3}{14}p-\frac{42}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{14}{9}a-\frac{3}{14}p-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{13}{20})(\frac{17}{15}+q)& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{q}+\color{blue}{\frac{17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{17}{15})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{17}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{15}x-\frac{13}{20}q-\frac{13}{20}.\frac{17}{15}& \text{Uitwerken } \\ & =qx+\frac{17}{15}x-\frac{13}{20}q-\frac{221}{300} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-8}{3}+x)(\frac{-1}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{-8}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}x-\frac{8}{3}b+\frac{8}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}x-\frac{8}{3}b+\frac{8}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{2}x-\frac{8}{3}b+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{6}{20}-b)(p+\frac{7}{20})& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{20}b+\frac{3}{10}p+\frac{3}{10}.\frac{7}{20}& \text{Uitwerken } \\ & =-bp-\frac{7}{20}b+\frac{3}{10}p+\frac{21}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{17}{4}+q)(x-\frac{-7}{17})& =(\color{red}{q}+\color{orange}{\frac{17}{4}}).(\color{green}{x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{17}q+\frac{17}{4}x+\frac{17}{4}.\frac{7}{17}& \text{Uitwerken } \\ & =qx+\frac{7}{17}q+\frac{17}{4}x+\frac{119}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{7}{17}q+\frac{17}{4}x+\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p-\frac{-19}{9})(\frac{-3}{19}-x)& =(\color{red}{p}+\color{orange}{\frac{19}{9}}).(\color{green}{-x}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(\frac{19}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{19}p-\frac{19}{9}x-\frac{19}{9}.\frac{3}{19}& \text{Uitwerken } \\ & =-px-\frac{3}{19}p-\frac{19}{9}x-\frac{57}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{3}{19}p-\frac{19}{9}x-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x-\frac{9}{19})(\frac{6}{7}-a)& =(\color{red}{x}+\color{orange}{\frac{-9}{19}}).(\color{green}{-a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{6}{7}x+\frac{9}{19}a-\frac{9}{19}.\frac{6}{7}& \text{Uitwerken } \\ & =-ax+\frac{6}{7}x+\frac{9}{19}a-\frac{54}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{16}{4}+q)(q+\frac{17}{3})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{3}q+4q+4.\frac{17}{3}& \text{Uitwerken } \\ & =q^2+(\frac{17}{3}+4)q+\frac{68}{3} & \text{Neem samen} \\ &=q^2+\frac{29}{3}q+\frac{68}{3} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(a-\frac{-5}{2})(\frac{5}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{13}a+\frac{5}{2}b+\frac{5}{2}.\frac{5}{13}& \text{Uitwerken } \\ & =ab+\frac{5}{13}a+\frac{5}{2}b+\frac{25}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{20}{13}-a)(x-\frac{-12}{11})& =(\color{red}{-a}+\color{orange}{\frac{20}{13}}).(\color{green}{x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{12}{11}a+\frac{20}{13}x+\frac{20}{13}.\frac{12}{11}& \text{Uitwerken } \\ & =-ax-\frac{12}{11}a+\frac{20}{13}x+\frac{240}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-13}{19})(\frac{14}{18}-b)& =(\color{red}{x}+\color{orange}{\frac{13}{19}}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}x-\frac{13}{19}b+\frac{13}{19}.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}x-\frac{13}{19}b+\frac{91}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{13}{19}+a)(q-\frac{18}{2})& =(\color{red}{a}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-9)} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = aq-9a+\frac{13}{19}q-\frac{13}{19}.9& \text{Uitwerken } \\ & =aq-9a+\frac{13}{19}q-\frac{117}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)