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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{2}-b)(\frac{8}{10}-x)& =(\color{red}{-b}+\color{orange}{(-5)}).(\color{green}{-x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-5)} . \color{green}{(-x)} + \color{orange}{(-5)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{5}b+5x-5.\frac{4}{5}& \text{Uitwerken } \\ & =bx-\frac{4}{5}b+5x-\frac{20}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{5}b+5x-4 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{16}{9}+p)(\frac{-4}{18}-q)& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{-q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{16}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{9}p-\frac{16}{9}q-\frac{16}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =-pq-\frac{2}{9}p-\frac{16}{9}q-\frac{32}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{6}{6})(\frac{-1}{8}-b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{8}p-1b-1.\frac{1}{8}& \text{Uitwerken } \\ & =-bp-\frac{1}{8}p-1b-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{-18}{14})(b+\frac{-6}{15})& =(\color{red}{a}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{5}a+\frac{9}{7}b-\frac{9}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =ab-\frac{2}{5}a+\frac{9}{7}b-\frac{18}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-2}{6})(\frac{17}{7}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{7}p-\frac{1}{3}q-\frac{1}{3}.\frac{17}{7}& \text{Uitwerken } \\ & =pq+\frac{17}{7}p-\frac{1}{3}q-\frac{17}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-13}{2}+b)(a+\frac{-4}{20})& =(\color{red}{b}+\color{orange}{\frac{-13}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{5}b-\frac{13}{2}a+\frac{13}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =ab-\frac{1}{5}b-\frac{13}{2}a+\frac{13}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{15}{20})(\frac{6}{16}+p)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{8}x+\frac{3}{4}p+\frac{3}{4}.\frac{3}{8}& \text{Uitwerken } \\ & =px+\frac{3}{8}x+\frac{3}{4}p+\frac{9}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-9}{2})(b+\frac{-6}{5})& =(\color{red}{p}+\color{orange}{\frac{9}{2}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{9}{2})} . \color{green}{(b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{5}p+\frac{9}{2}b-\frac{9}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =bp-\frac{6}{5}p+\frac{9}{2}b-\frac{54}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{5}p+\frac{9}{2}b-\frac{27}{5} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{5}{3}+a)(\frac{-1}{12}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{12}a+\frac{5}{3}a-\frac{5}{3}.\frac{1}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{12})+\frac{5}{3})a-(\frac{-5}{36}) & \text{Neem samen} \\ &=a^2+\frac{19}{12}a-(\frac{-5}{36}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a-\frac{-19}{16})(b-\frac{8}{5})& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{19}{16})} . \color{green}{(b)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{5}a+\frac{19}{16}b-\frac{19}{16}.\frac{8}{5}& \text{Uitwerken } \\ & =ab-\frac{8}{5}a+\frac{19}{16}b-\frac{152}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{8}{5}a+\frac{19}{16}b-\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{3}{19})(\frac{-8}{20}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{19}}).(\color{green}{a}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{5}q-\frac{3}{19}a+\frac{3}{19}.\frac{2}{5}& \text{Uitwerken } \\ & =aq-\frac{2}{5}q-\frac{3}{19}a+\frac{6}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{20}{6}+q)(q-\frac{-18}{18})& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq+1q+\frac{10}{3}q+\frac{10}{3}.1& \text{Uitwerken } \\ & =q^2+(1+\frac{10}{3})q+\frac{10}{3} & \text{Neem samen} \\ &=q^2+\frac{13}{3}q+\frac{10}{3} & \text{Maak de som} \\\end{align}\)