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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{-9}{9})(\frac{-17}{10}-x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{10}q-1x-1.\frac{17}{10}& \text{Uitwerken } \\ & =-qx-\frac{17}{10}q-1x-\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-5}{14}-b)(x-\frac{-14}{3})& =(\color{red}{-b}+\color{orange}{\frac{-5}{14}}).(\color{green}{x}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{14}{3}b-\frac{5}{14}x-\frac{5}{14}.\frac{14}{3}& \text{Uitwerken } \\ & =-bx-\frac{14}{3}b-\frac{5}{14}x-\frac{70}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{14}{3}b-\frac{5}{14}x-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{13}{19}+b)(\frac{10}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{13}{19}}).(\color{green}{-b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{5}{9}b-\frac{13}{19}b+\frac{13}{19}.\frac{5}{9}& \text{Uitwerken } \\ & =-b^2+(\frac{5}{9}+(\frac{-13}{19}))b+(\frac{-65}{171}) & \text{Neem samen} \\ &=-b^2-\frac{22}{171}b+(\frac{-65}{171}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-19}{5}+q)(a+\frac{-18}{13})& =(\color{red}{q}+\color{orange}{\frac{-19}{5}}).(\color{green}{a}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{13}q-\frac{19}{5}a+\frac{19}{5}.\frac{18}{13}& \text{Uitwerken } \\ & =aq-\frac{18}{13}q-\frac{19}{5}a+\frac{342}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{12}+b)(p-\frac{-19}{2})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{2}b+\frac{3}{2}p+\frac{3}{2}.\frac{19}{2}& \text{Uitwerken } \\ & =bp+\frac{19}{2}b+\frac{3}{2}p+\frac{57}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{13}{13})(\frac{18}{5}-b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{18}{5}a+1b-1.\frac{18}{5}& \text{Uitwerken } \\ & =-ab+\frac{18}{5}a+1b-\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{-12}{16})(q+\frac{3}{17})& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{17}a+\frac{3}{4}q+\frac{3}{4}.\frac{3}{17}& \text{Uitwerken } \\ & =aq+\frac{3}{17}a+\frac{3}{4}q+\frac{9}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}((-13)-a)(\frac{-2}{13}+p)& =(\color{red}{-a}+\color{orange}{(-13)}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(-13)} . \color{green}{(p)} + \color{orange}{(-13)} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{13}a-13p+13.\frac{2}{13}& \text{Uitwerken } \\ & =-ap+\frac{2}{13}a-13p+\frac{26}{13} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{13}a-13p+2 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b-\frac{-4}{11})(p+\frac{-3}{3})& =(\color{red}{b}+\color{orange}{\frac{4}{11}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{4}{11})} . \color{green}{(p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1b+\frac{4}{11}p-\frac{4}{11}.1& \text{Uitwerken } \\ & =bp-1b+\frac{4}{11}p-\frac{4}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{4}+x)(\frac{6}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{7}x-\frac{5}{4}a-\frac{5}{4}.\frac{3}{7}& \text{Uitwerken } \\ & =ax+\frac{3}{7}x-\frac{5}{4}a-\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-7}{10})(a-\frac{-15}{15})& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{7}{10}a-\frac{7}{10}.1& \text{Uitwerken } \\ & =ap+1p-\frac{7}{10}a-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{-12}{2})(\frac{5}{15}+b)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-6)} . \color{green}{(b)} + \color{orange}{(-6)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}a-6b-6.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}a-6b-\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{3}a-6b-2 & \text{Vereenvoudig} \\\end{align}\)