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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{7}{15}+b)(q-\frac{-4}{4})& =(\color{red}{b}+\color{orange}{\frac{7}{15}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b+\frac{7}{15}q+\frac{7}{15}.1& \text{Uitwerken } \\ & =bq+1b+\frac{7}{15}q+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-4}{7})(\frac{-20}{13}-x)& =(\color{red}{b}+\color{orange}{\frac{4}{7}}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{4}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{20}{13}b-\frac{4}{7}x-\frac{4}{7}.\frac{20}{13}& \text{Uitwerken } \\ & =-bx-\frac{20}{13}b-\frac{4}{7}x-\frac{80}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{4}{15}+a)(x-\frac{-7}{14})& =(\color{red}{a}+\color{orange}{\frac{4}{15}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{4}{15})} . \color{green}{(x)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a+\frac{4}{15}x+\frac{4}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a+\frac{4}{15}x+\frac{4}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}a+\frac{4}{15}x+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{-7}{18})(x+\frac{9}{3})& =(\color{red}{b}+\color{orange}{\frac{-7}{18}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{-7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bx+3b-\frac{7}{18}x-\frac{7}{18}.3& \text{Uitwerken } \\ & =bx+3b-\frac{7}{18}x-\frac{21}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+3b-\frac{7}{18}x-\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{13}{20}+x)(x+\frac{12}{20})& =(\color{red}{x}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{5}x+\frac{13}{20}x+\frac{13}{20}.\frac{3}{5}& \text{Uitwerken } \\ & =x^2+(\frac{3}{5}+\frac{13}{20})x+\frac{39}{100} & \text{Neem samen} \\ &=x^2+\frac{25}{20}x+\frac{39}{100} & \text{Maak de som} \\ &=x^2+\frac{5}{4}x+\frac{39}{100} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
6. \(\begin{align}(a+\frac{-12}{8})(\frac{-9}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{11})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-9}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{9}{11}a+\frac{3}{2}x+\frac{3}{2}.\frac{9}{11}& \text{Uitwerken } \\ & =-ax-\frac{9}{11}a+\frac{3}{2}x+\frac{27}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{10}{16})(b+\frac{-3}{11})& =(\color{red}{q}+\color{orange}{\frac{5}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{11}q+\frac{5}{8}b-\frac{5}{8}.\frac{3}{11}& \text{Uitwerken } \\ & =bq-\frac{3}{11}q+\frac{5}{8}b-\frac{15}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-12}{11})(b-\frac{-15}{15})& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{11})} . \color{green}{(b)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a+\frac{12}{11}b+\frac{12}{11}.1& \text{Uitwerken } \\ & =ab+1a+\frac{12}{11}b+\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{4}{8})(\frac{-17}{4}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{17}{4}q-\frac{1}{2}p-\frac{1}{2}.\frac{17}{4}& \text{Uitwerken } \\ & =-pq-\frac{17}{4}q-\frac{1}{2}p-\frac{17}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-9}{3})(\frac{18}{3}+p)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(6)} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = px+6x+3p+3.6& \text{Uitwerken } \\ & =px+6x+3p+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-12}{19}-a)(x+13)& =(\color{red}{-a}+\color{orange}{\frac{-12}{19}}).(\color{green}{x}+\color{blue}{13})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(13)} + \color{orange}{(\frac{-12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = -ax-13a-\frac{12}{19}x-\frac{12}{19}.13& \text{Uitwerken } \\ & =-ax-13a-\frac{12}{19}x-\frac{156}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{-10}{17})(p+\frac{20}{19})& =(\color{red}{x}+\color{orange}{\frac{-10}{17}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{19}x-\frac{10}{17}p-\frac{10}{17}.\frac{20}{19}& \text{Uitwerken } \\ & =px+\frac{20}{19}x-\frac{10}{17}p-\frac{200}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)