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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{3}-b)(\frac{12}{11}+q)& =(\color{red}{-b}+\color{orange}{\frac{-5}{3}}).(\color{green}{q}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{12}{11}b-\frac{5}{3}q-\frac{5}{3}.\frac{12}{11}& \text{Uitwerken } \\ & =-bq-\frac{12}{11}b-\frac{5}{3}q-\frac{60}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{12}{11}b-\frac{5}{3}q-\frac{20}{11} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-16}{17}-p)(\frac{-1}{15}-p)& =(\color{red}{-p}+\color{orange}{\frac{-16}{17}}).(\color{green}{-p}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{15}p+\frac{16}{17}p+\frac{16}{17}.\frac{1}{15}& \text{Uitwerken } \\ & =p^2+(\frac{1}{15}+\frac{16}{17})p+\frac{16}{255} & \text{Neem samen} \\ &=p^2+\frac{257}{255}p+\frac{16}{255} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-18}{18}-a)(\frac{-9}{20}-a)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{20}a+1a+1.\frac{9}{20}& \text{Uitwerken } \\ & =a^2+(\frac{9}{20}+1)a+\frac{9}{20} & \text{Neem samen} \\ &=a^2+\frac{29}{20}a+\frac{9}{20} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q+\frac{-5}{18})(x+\frac{9}{3})& =(\color{red}{q}+\color{orange}{\frac{-5}{18}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-5}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qx+3q-\frac{5}{18}x-\frac{5}{18}.3& \text{Uitwerken } \\ & =qx+3q-\frac{5}{18}x-\frac{15}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+3q-\frac{5}{18}x-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{15}{2}-b)(\frac{8}{17}-p)& =(\color{red}{-b}+\color{orange}{\frac{15}{2}}).(\color{green}{-p}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{15}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{17}b-\frac{15}{2}p+\frac{15}{2}.\frac{8}{17}& \text{Uitwerken } \\ & =bp-\frac{8}{17}b-\frac{15}{2}p+\frac{120}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{8}{17}b-\frac{15}{2}p+\frac{60}{17} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{3}{6}+b)(\frac{11}{16}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{16}b+\frac{1}{2}q+\frac{1}{2}.\frac{11}{16}& \text{Uitwerken } \\ & =bq+\frac{11}{16}b+\frac{1}{2}q+\frac{11}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{17}{7})(\frac{4}{8}+q)& =(\color{red}{q}+\color{orange}{\frac{-17}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-17}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{1}{2}q-\frac{17}{7}q-\frac{17}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+(\frac{1}{2}+(\frac{-17}{7}))q-(\frac{-17}{14}) & \text{Neem samen} \\ &=q^2-\frac{27}{14}q-(\frac{-17}{14}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a+\frac{16}{11})(\frac{-18}{13}-b)& =(\color{red}{a}+\color{orange}{\frac{16}{11}}).(\color{green}{-b}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{16}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{18}{13}a-\frac{16}{11}b-\frac{16}{11}.\frac{18}{13}& \text{Uitwerken } \\ & =-ab-\frac{18}{13}a-\frac{16}{11}b-\frac{288}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{17}{8}+x)(\frac{8}{15}-a)& =(\color{red}{x}+\color{orange}{\frac{17}{8}}).(\color{green}{-a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{17}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{8}{15}x-\frac{17}{8}a+\frac{17}{8}.\frac{8}{15}& \text{Uitwerken } \\ & =-ax+\frac{8}{15}x-\frac{17}{8}a+\frac{136}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{8}{15}x-\frac{17}{8}a+\frac{17}{15} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{16}+x)(a-\frac{5}{18})& =(\color{red}{x}+\color{orange}{\frac{-3}{16}}).(\color{green}{a}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{18}x-\frac{3}{16}a+\frac{3}{16}.\frac{5}{18}& \text{Uitwerken } \\ & =ax-\frac{5}{18}x-\frac{3}{16}a+\frac{15}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{18}x-\frac{3}{16}a+\frac{5}{96} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{5}{12})(b-\frac{-8}{17})& =(\color{red}{x}+\color{orange}{\frac{-5}{12}}).(\color{green}{b}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{17}x-\frac{5}{12}b-\frac{5}{12}.\frac{8}{17}& \text{Uitwerken } \\ & =bx+\frac{8}{17}x-\frac{5}{12}b-\frac{40}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{8}{17}x-\frac{5}{12}b-\frac{10}{51} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{-18}{18})(\frac{-13}{3}-q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{13}{3}x-1q-1.\frac{13}{3}& \text{Uitwerken } \\ & =-qx-\frac{13}{3}x-1q-\frac{13}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)