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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{11}{18})(p+\frac{-3}{12})& =(\color{red}{q}+\color{orange}{\frac{-11}{18}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{4}q-\frac{11}{18}p+\frac{11}{18}.\frac{1}{4}& \text{Uitwerken } \\ & =pq-\frac{1}{4}q-\frac{11}{18}p+\frac{11}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{-6}{2})(p-\frac{6}{9})& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}a-3p+3.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}a-3p+\frac{6}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{3}a-3p+2 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{16}+p)(\frac{10}{15}+p)& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{2}{3}p-\frac{13}{16}p-\frac{13}{16}.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+(\frac{2}{3}+(\frac{-13}{16}))p-(\frac{-26}{48}) & \text{Neem samen} \\ &=p^2-\frac{7}{48}p-(\frac{-26}{48}) & \text{Maak de som} \\ &=p^2-\frac{7}{48}p+\frac{13}{24} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(q-\frac{-7}{11})(x-\frac{20}{5})& =(\color{red}{q}+\color{orange}{\frac{7}{11}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{7}{11})} . \color{green}{(x)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4q+\frac{7}{11}x-\frac{7}{11}.4& \text{Uitwerken } \\ & =qx-4q+\frac{7}{11}x-\frac{28}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{9}+b)(p+\frac{-7}{13})& =(\color{red}{b}+\color{orange}{\frac{-16}{9}}).(\color{green}{p}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{13}b-\frac{16}{9}p+\frac{16}{9}.\frac{7}{13}& \text{Uitwerken } \\ & =bp-\frac{7}{13}b-\frac{16}{9}p+\frac{112}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{2}{6}+b)(b-\frac{-11}{3})& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{3}b+\frac{1}{3}b+\frac{1}{3}.\frac{11}{3}& \text{Uitwerken } \\ & =b^2+(\frac{11}{3}+\frac{1}{3})b+\frac{11}{9} & \text{Neem samen} \\ &=b^2+\frac{12}{3}b+\frac{11}{9} & \text{Maak de som} \\ &=b^2+4b+\frac{11}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{15}{14}-a)(b-\frac{-1}{4})& =(\color{red}{-a}+\color{orange}{\frac{15}{14}}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{15}{14})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{4}a+\frac{15}{14}b+\frac{15}{14}.\frac{1}{4}& \text{Uitwerken } \\ & =-ab-\frac{1}{4}a+\frac{15}{14}b+\frac{15}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-16}{4}-q)(a+\frac{8}{12})& =(\color{red}{-q}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{2}{3}q-4a-4.\frac{2}{3}& \text{Uitwerken } \\ & =-aq-\frac{2}{3}q-4a-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-12}{6}+b)(\frac{2}{16}-b)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{8}b+2b-2.\frac{1}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{8}+2)b-\frac{2}{8} & \text{Neem samen} \\ &=-b^2+\frac{17}{8}b-\frac{2}{8} & \text{Maak de som} \\ &=-b^2+\frac{17}{8}b-\frac{1}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(q-\frac{-3}{15})(b+\frac{-9}{9})& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1q+\frac{1}{5}b-\frac{1}{5}.1& \text{Uitwerken } \\ & =bq-1q+\frac{1}{5}b-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{17}{8}+q)(\frac{16}{20}-x)& =(\color{red}{q}+\color{orange}{\frac{17}{8}}).(\color{green}{-x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{17}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{4}{5}q-\frac{17}{8}x+\frac{17}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =-qx+\frac{4}{5}q-\frac{17}{8}x+\frac{68}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{4}{5}q-\frac{17}{8}x+\frac{17}{10} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{6}{2}+a)(p-\frac{7}{17})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{17}a+3p-3.\frac{7}{17}& \text{Uitwerken } \\ & =ap-\frac{7}{17}a+3p-\frac{21}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)