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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-12}{4})(b-\frac{1}{17})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{17}b-3b+3.\frac{1}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{17})+(-3))b+\frac{3}{17} & \text{Neem samen} \\ &=b^2-\frac{52}{17}b+\frac{3}{17} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(b+\frac{-20}{17})(p-(-6))& =(\color{red}{b}+\color{orange}{\frac{-20}{17}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{-20}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bp+6b-\frac{20}{17}p-\frac{20}{17}.6& \text{Uitwerken } \\ & =bp+6b-\frac{20}{17}p-\frac{120}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-15}{12}-q)(q+\frac{13}{6})& =(\color{red}{-q}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{13}{6}q-\frac{5}{4}q-\frac{5}{4}.\frac{13}{6}& \text{Uitwerken } \\ & =-q^2+((\frac{-13}{6})+(\frac{-5}{4}))q-\frac{65}{24} & \text{Neem samen} \\ &=-q^2-\frac{41}{12}q-\frac{65}{24} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(a+\frac{2}{3})(\frac{17}{4}+x)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{4}a+\frac{2}{3}x+\frac{2}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =ax+\frac{17}{4}a+\frac{2}{3}x+\frac{34}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{4}a+\frac{2}{3}x+\frac{17}{6} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+(-14))(\frac{-20}{9}+p)& =(\color{red}{p}+\color{orange}{(-14)}).(\color{green}{p}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(-14)} . \color{green}{(p)} + \color{orange}{(-14)} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{20}{9}p-14p+14.\frac{20}{9}& \text{Uitwerken } \\ & =p^2+((\frac{-20}{9})+(-14))p+\frac{280}{9} & \text{Neem samen} \\ &=p^2-\frac{146}{9}p+\frac{280}{9} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(q+\frac{4}{8})(q+\frac{-8}{8})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q+\frac{1}{2}q-\frac{1}{2}.1& \text{Uitwerken } \\ & =q^2+((-1)+\frac{1}{2})q-(\frac{-1}{2}) & \text{Neem samen} \\ &=q^2-\frac{1}{2}q-(\frac{-1}{2}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(b+\frac{1}{4})(\frac{2}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b+\frac{1}{4}a+\frac{1}{4}.1& \text{Uitwerken } \\ & =ab+1b+\frac{1}{4}a+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{2}{16}+x)(\frac{-8}{3}-b)& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{-b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{3}x-\frac{1}{8}b-\frac{1}{8}.\frac{8}{3}& \text{Uitwerken } \\ & =-bx-\frac{8}{3}x-\frac{1}{8}b-\frac{8}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{3}x-\frac{1}{8}b-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{10}{12})(\frac{14}{19}-q)& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{-q}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{14}{19}q+\frac{5}{6}q-\frac{5}{6}.\frac{14}{19}& \text{Uitwerken } \\ & =-q^2+(\frac{14}{19}+\frac{5}{6})q-\frac{70}{114} & \text{Neem samen} \\ &=-q^2+\frac{179}{114}q-\frac{70}{114} & \text{Maak de som} \\ &=-q^2+\frac{179}{114}q-\frac{35}{57} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{7}{18}+a)(b+\frac{-15}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{18}}).(\color{green}{b}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{2}a+\frac{7}{18}b-\frac{7}{18}.\frac{15}{2}& \text{Uitwerken } \\ & =ab-\frac{15}{2}a+\frac{7}{18}b-\frac{105}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{15}{2}a+\frac{7}{18}b-\frac{35}{12} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{13}{6}+a)(\frac{-11}{4}+x)& =(\color{red}{a}+\color{orange}{\frac{13}{6}}).(\color{green}{x}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{13}{6})} . \color{green}{(x)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{4}a+\frac{13}{6}x-\frac{13}{6}.\frac{11}{4}& \text{Uitwerken } \\ & =ax-\frac{11}{4}a+\frac{13}{6}x-\frac{143}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{18}{6}+p)(\frac{9}{14}+q)& =(\color{red}{p}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{14}p+3q+3.\frac{9}{14}& \text{Uitwerken } \\ & =pq+\frac{9}{14}p+3q+\frac{27}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)