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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-6}{3})(p-\frac{-18}{16})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{8}a+2p+2.\frac{9}{8}& \text{Uitwerken } \\ & =ap+\frac{9}{8}a+2p+\frac{18}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{8}a+2p+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-11}{6}-p)(\frac{2}{18}+a)& =(\color{red}{-p}+\color{orange}{\frac{-11}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{9}p-\frac{11}{6}a-\frac{11}{6}.\frac{1}{9}& \text{Uitwerken } \\ & =-ap-\frac{1}{9}p-\frac{11}{6}a-\frac{11}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-8}{15}-b)(x-\frac{13}{20})& =(\color{red}{-b}+\color{orange}{\frac{-8}{15}}).(\color{green}{x}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{15})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{20}b-\frac{8}{15}x+\frac{8}{15}.\frac{13}{20}& \text{Uitwerken } \\ & =-bx+\frac{13}{20}b-\frac{8}{15}x+\frac{104}{300} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{13}{20}b-\frac{8}{15}x+\frac{26}{75} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{5}{11})(\frac{9}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{5}{11}}).(\color{green}{-x}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{5}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -px+3p-\frac{5}{11}x+\frac{5}{11}.3& \text{Uitwerken } \\ & =-px+3p-\frac{5}{11}x+\frac{15}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{8}{18}+b)(\frac{13}{17}-q)& =(\color{red}{b}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{17}b-\frac{4}{9}q+\frac{4}{9}.\frac{13}{17}& \text{Uitwerken } \\ & =-bq+\frac{13}{17}b-\frac{4}{9}q+\frac{52}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{2}{19})(x-\frac{-11}{12})& =(\color{red}{p}+\color{orange}{\frac{2}{19}}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{2}{19})} . \color{green}{(x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{12}p+\frac{2}{19}x+\frac{2}{19}.\frac{11}{12}& \text{Uitwerken } \\ & =px+\frac{11}{12}p+\frac{2}{19}x+\frac{22}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{11}{12}p+\frac{2}{19}x+\frac{11}{114} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{6}{10}-b)(x-\frac{-17}{3})& =(\color{red}{-b}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{17}{3}b+\frac{3}{5}x+\frac{3}{5}.\frac{17}{3}& \text{Uitwerken } \\ & =-bx-\frac{17}{3}b+\frac{3}{5}x+\frac{51}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{17}{3}b+\frac{3}{5}x+\frac{17}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{20}-x)(\frac{-1}{20}+q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{20}x-\frac{1}{10}q+\frac{1}{10}.\frac{1}{20}& \text{Uitwerken } \\ & =-qx+\frac{1}{20}x-\frac{1}{10}q+\frac{1}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{5}{4}+p)(q+\frac{-19}{9})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{9}p+\frac{5}{4}q-\frac{5}{4}.\frac{19}{9}& \text{Uitwerken } \\ & =pq-\frac{19}{9}p+\frac{5}{4}q-\frac{95}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p+(-5))(q-16)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-16)} + \color{orange}{(-5)} . \color{green}{(q)} + \color{orange}{(-5)} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = pq-16p-5q+5.16& \text{Uitwerken } \\ & =pq-16p-5q+80 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-1)(x-\frac{-1}{14})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{14}x-1x-1.\frac{1}{14}& \text{Uitwerken } \\ & =x^2+(\frac{1}{14}+(-1))x-(\frac{-1}{14}) & \text{Neem samen} \\ &=x^2-\frac{13}{14}x-(\frac{-1}{14}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(a+\frac{7}{20})(\frac{3}{19}+a)& =(\color{red}{a}+\color{orange}{\frac{7}{20}}).(\color{green}{a}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{19}a+\frac{7}{20}a+\frac{7}{20}.\frac{3}{19}& \text{Uitwerken } \\ & =a^2+(\frac{3}{19}+\frac{7}{20})a+\frac{21}{380} & \text{Neem samen} \\ &=a^2+\frac{193}{380}a+\frac{21}{380} & \text{Maak de som} \\\end{align}\)