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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{8}{6}+q)(a+7)& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(7)} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = aq+7q+\frac{4}{3}a+\frac{4}{3}.7& \text{Uitwerken } \\ & =aq+7q+\frac{4}{3}a+\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{13}{10})(p-\frac{10}{7})& =(\color{red}{x}+\color{orange}{\frac{13}{10}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{13}{10})} . \color{green}{(p)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{10}{7}x+\frac{13}{10}p-\frac{13}{10}.\frac{10}{7}& \text{Uitwerken } \\ & =px-\frac{10}{7}x+\frac{13}{10}p-\frac{130}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{10}{7}x+\frac{13}{10}p-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{-14}{10})(\frac{6}{9}-q)& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{-q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{3}b+\frac{7}{5}q-\frac{7}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-bq+\frac{2}{3}b+\frac{7}{5}q-\frac{14}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{12}{15})(b-\frac{10}{18})& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{9}p+\frac{4}{5}b-\frac{4}{5}.\frac{5}{9}& \text{Uitwerken } \\ & =bp-\frac{5}{9}p+\frac{4}{5}b-\frac{20}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{9}p+\frac{4}{5}b-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{14}{4}+a)(q-\frac{-4}{2})& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aq+2a+\frac{7}{2}q+\frac{7}{2}.2& \text{Uitwerken } \\ & =aq+2a+\frac{7}{2}q+\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+2a+\frac{7}{2}q+7 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{1}{20})(x+\frac{-6}{10})& =(\color{red}{b}+\color{orange}{\frac{1}{20}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{5}b+\frac{1}{20}x-\frac{1}{20}.\frac{3}{5}& \text{Uitwerken } \\ & =bx-\frac{3}{5}b+\frac{1}{20}x-\frac{3}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{20}{12})(\frac{-16}{4}+a)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ap-4p+\frac{5}{3}a-\frac{5}{3}.4& \text{Uitwerken } \\ & =ap-4p+\frac{5}{3}a-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{9}{17}-b)(\frac{-7}{14}-b)& =(\color{red}{-b}+\color{orange}{\frac{9}{17}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{9}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{2}b-\frac{9}{17}b-\frac{9}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =b^2+(\frac{1}{2}+(\frac{-9}{17}))b-(\frac{-9}{34}) & \text{Neem samen} \\ &=b^2-\frac{1}{34}b-(\frac{-9}{34}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{16}{3}+a)(\frac{-14}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{3}a+\frac{16}{3}p-\frac{16}{3}.\frac{7}{3}& \text{Uitwerken } \\ & =ap-\frac{7}{3}a+\frac{16}{3}p-\frac{112}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{12}{9}-b)(p-\frac{17}{3})& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{3}b+\frac{4}{3}p-\frac{4}{3}.\frac{17}{3}& \text{Uitwerken } \\ & =-bp+\frac{17}{3}b+\frac{4}{3}p-\frac{68}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{7}{8})(\frac{16}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{-a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{9}b+\frac{7}{8}a-\frac{7}{8}.\frac{8}{9}& \text{Uitwerken } \\ & =-ab+\frac{8}{9}b+\frac{7}{8}a-\frac{56}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{8}{9}b+\frac{7}{8}a-\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-17}{3}+q)(b+\frac{-2}{13})& =(\color{red}{q}+\color{orange}{\frac{-17}{3}}).(\color{green}{b}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{13}q-\frac{17}{3}b+\frac{17}{3}.\frac{2}{13}& \text{Uitwerken } \\ & =bq-\frac{2}{13}q-\frac{17}{3}b+\frac{34}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)