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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{20}+x)(q-\frac{-16}{20})& =(\color{red}{x}+\color{orange}{\frac{-19}{20}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{5}x-\frac{19}{20}q-\frac{19}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =qx+\frac{4}{5}x-\frac{19}{20}q-\frac{76}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{5}x-\frac{19}{20}q-\frac{19}{25} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-6}{11}+b)(a-\frac{-1}{12})& =(\color{red}{b}+\color{orange}{\frac{-6}{11}}).(\color{green}{a}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{12}b-\frac{6}{11}a-\frac{6}{11}.\frac{1}{12}& \text{Uitwerken } \\ & =ab+\frac{1}{12}b-\frac{6}{11}a-\frac{6}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{12}b-\frac{6}{11}a-\frac{1}{22} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{9}{19}+p)(\frac{19}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{9}{19}}).(\color{green}{-q}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{5}p-\frac{9}{19}q+\frac{9}{19}.\frac{19}{5}& \text{Uitwerken } \\ & =-pq+\frac{19}{5}p-\frac{9}{19}q+\frac{171}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{19}{5}p-\frac{9}{19}q+\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-15}{15}+q)(\frac{-7}{11}+q)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{7}{11}q-1q+1.\frac{7}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-7}{11})+(-1))q+\frac{7}{11} & \text{Neem samen} \\ &=q^2-\frac{18}{11}q+\frac{7}{11} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{-17}{17}+x)(x+\frac{-3}{18})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{6}x-1x+1.\frac{1}{6}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{6})+(-1))x+\frac{1}{6} & \text{Neem samen} \\ &=x^2-\frac{7}{6}x+\frac{1}{6} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{16}{7}+a)(p-\frac{-7}{13})& =(\color{red}{a}+\color{orange}{\frac{16}{7}}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{16}{7})} . \color{green}{(p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{13}a+\frac{16}{7}p+\frac{16}{7}.\frac{7}{13}& \text{Uitwerken } \\ & =ap+\frac{7}{13}a+\frac{16}{7}p+\frac{112}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{7}{13}a+\frac{16}{7}p+\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(p+\frac{-9}{7})(\frac{-2}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{3}p-\frac{9}{7}q+\frac{9}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =pq-\frac{2}{3}p-\frac{9}{7}q+\frac{18}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{3}p-\frac{9}{7}q+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{16}-b)(\frac{17}{20}+a)& =(\color{red}{-b}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{20}b-\frac{1}{8}a-\frac{1}{8}.\frac{17}{20}& \text{Uitwerken } \\ & =-ab-\frac{17}{20}b-\frac{1}{8}a-\frac{17}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q-\frac{1}{18})(a+\frac{1}{13})& =(\color{red}{q}+\color{orange}{\frac{-1}{18}}).(\color{green}{a}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{13}q-\frac{1}{18}a-\frac{1}{18}.\frac{1}{13}& \text{Uitwerken } \\ & =aq+\frac{1}{13}q-\frac{1}{18}a-\frac{1}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-7}{11}+p)(x+\frac{-8}{14})& =(\color{red}{p}+\color{orange}{\frac{-7}{11}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{7}p-\frac{7}{11}x+\frac{7}{11}.\frac{4}{7}& \text{Uitwerken } \\ & =px-\frac{4}{7}p-\frac{7}{11}x+\frac{28}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{7}p-\frac{7}{11}x+\frac{4}{11} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-10)(\frac{-20}{20}-x)& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(-10)} . \color{green}{(-x)} + \color{orange}{(-10)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b+10x+10.1& \text{Uitwerken } \\ & =-bx-1b+10x+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-13}{16})(b-\frac{-8}{17})& =(\color{red}{p}+\color{orange}{\frac{-13}{16}}).(\color{green}{b}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{17}p-\frac{13}{16}b-\frac{13}{16}.\frac{8}{17}& \text{Uitwerken } \\ & =bp+\frac{8}{17}p-\frac{13}{16}b-\frac{104}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{8}{17}p-\frac{13}{16}b-\frac{13}{34} & \text{Vereenvoudig} \\\end{align}\)