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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-11}{16})(\frac{-14}{16}-b)& =(\color{red}{p}+\color{orange}{\frac{11}{16}}).(\color{green}{-b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{11}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{8}p-\frac{11}{16}b-\frac{11}{16}.\frac{7}{8}& \text{Uitwerken } \\ & =-bp-\frac{7}{8}p-\frac{11}{16}b-\frac{77}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{17}{8})(\frac{19}{19}-b)& =(\color{red}{q}+\color{orange}{\frac{-17}{8}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{-17}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq+1q+\frac{17}{8}b-\frac{17}{8}.1& \text{Uitwerken } \\ & =-bq+1q+\frac{17}{8}b-\frac{17}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-13}{17})(\frac{-9}{9}+b)& =(\color{red}{p}+\color{orange}{\frac{-13}{17}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{13}{17}b+\frac{13}{17}.1& \text{Uitwerken } \\ & =bp-1p-\frac{13}{17}b+\frac{13}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+(-4))(\frac{5}{11}+x)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{11}q-4x-4.\frac{5}{11}& \text{Uitwerken } \\ & =qx+\frac{5}{11}q-4x-\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+(-8))(\frac{5}{15}+b)& =(\color{red}{x}+\color{orange}{(-8)}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-8)} . \color{green}{(b)} + \color{orange}{(-8)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{3}x-8b-8.\frac{1}{3}& \text{Uitwerken } \\ & =bx+\frac{1}{3}x-8b-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{17}{13}+p)(b-\frac{-6}{10})& =(\color{red}{p}+\color{orange}{\frac{17}{13}}).(\color{green}{b}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{17}{13})} . \color{green}{(b)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{5}p+\frac{17}{13}b+\frac{17}{13}.\frac{3}{5}& \text{Uitwerken } \\ & =bp+\frac{3}{5}p+\frac{17}{13}b+\frac{51}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{13}+q)(\frac{5}{4}+q)& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{5}{4}q-\frac{11}{13}q-\frac{11}{13}.\frac{5}{4}& \text{Uitwerken } \\ & =q^2+(\frac{5}{4}+(\frac{-11}{13}))q-(\frac{-55}{52}) & \text{Neem samen} \\ &=q^2+\frac{21}{52}q-(\frac{-55}{52}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{10}{11}+x)(a+\frac{14}{3})& =(\color{red}{x}+\color{orange}{\frac{10}{11}}).(\color{green}{a}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{14}{3}x+\frac{10}{11}a+\frac{10}{11}.\frac{14}{3}& \text{Uitwerken } \\ & =ax+\frac{14}{3}x+\frac{10}{11}a+\frac{140}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-2}{17}-a)(b-\frac{-20}{4})& =(\color{red}{-a}+\color{orange}{\frac{-2}{17}}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(5)} + \color{orange}{(\frac{-2}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ab-5a-\frac{2}{17}b-\frac{2}{17}.5& \text{Uitwerken } \\ & =-ab-5a-\frac{2}{17}b-\frac{10}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-20}{14}+p)(\frac{14}{17}+b)& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{b}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{17}p-\frac{10}{7}b-\frac{10}{7}.\frac{14}{17}& \text{Uitwerken } \\ & =bp+\frac{14}{17}p-\frac{10}{7}b-\frac{140}{119} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{17}p-\frac{10}{7}b-\frac{20}{17} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{-5}{15})(\frac{-17}{12}+a)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{12}b+\frac{1}{3}a-\frac{1}{3}.\frac{17}{12}& \text{Uitwerken } \\ & =ab-\frac{17}{12}b+\frac{1}{3}a-\frac{17}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{10}+p)(\frac{3}{17}+x)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{17}p-\frac{1}{2}x-\frac{1}{2}.\frac{3}{17}& \text{Uitwerken } \\ & =px+\frac{3}{17}p-\frac{1}{2}x-\frac{3}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)