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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{7}{18}-q)(\frac{9}{19}+x)& =(\color{red}{-q}+\color{orange}{\frac{7}{18}}).(\color{green}{x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{9}{19}q+\frac{7}{18}x+\frac{7}{18}.\frac{9}{19}& \text{Uitwerken } \\ & =-qx-\frac{9}{19}q+\frac{7}{18}x+\frac{63}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{9}{19}q+\frac{7}{18}x+\frac{7}{38} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{20}{12})(x-\frac{15}{17})& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{17}b-\frac{5}{3}x+\frac{5}{3}.\frac{15}{17}& \text{Uitwerken } \\ & =bx-\frac{15}{17}b-\frac{5}{3}x+\frac{75}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{17}b-\frac{5}{3}x+\frac{25}{17} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q+\frac{5}{13})(b-\frac{-8}{13})& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{b}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{5}{13})} . \color{green}{(b)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{13}q+\frac{5}{13}b+\frac{5}{13}.\frac{8}{13}& \text{Uitwerken } \\ & =bq+\frac{8}{13}q+\frac{5}{13}b+\frac{40}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{7}{4}-x)(b+\frac{-17}{5})& =(\color{red}{-x}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{5}x+\frac{7}{4}b-\frac{7}{4}.\frac{17}{5}& \text{Uitwerken } \\ & =-bx+\frac{17}{5}x+\frac{7}{4}b-\frac{119}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{8}{16}-a)(b-\frac{-9}{18})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a+\frac{1}{2}b+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a+\frac{1}{2}b+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-7}{20})(b-\frac{4}{5})& =(\color{red}{a}+\color{orange}{\frac{-7}{20}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{5}a-\frac{7}{20}b+\frac{7}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =ab-\frac{4}{5}a-\frac{7}{20}b+\frac{28}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{5}a-\frac{7}{20}b+\frac{7}{25} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b+3)(\frac{-20}{5}-p)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bp-4b-3p-3.4& \text{Uitwerken } \\ & =-bp-4b-3p-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{18}-p)(\frac{10}{17}+q)& =(\color{red}{-p}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{10}{17}p-\frac{1}{9}q-\frac{1}{9}.\frac{10}{17}& \text{Uitwerken } \\ & =-pq-\frac{10}{17}p-\frac{1}{9}q-\frac{10}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{17}-q)(\frac{-7}{15}-x)& =(\color{red}{-q}+\color{orange}{\frac{-18}{17}}).(\color{green}{-x}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{15}q+\frac{18}{17}x+\frac{18}{17}.\frac{7}{15}& \text{Uitwerken } \\ & =qx+\frac{7}{15}q+\frac{18}{17}x+\frac{126}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{7}{15}q+\frac{18}{17}x+\frac{42}{85} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{15}{15}+p)(\frac{12}{19}+x)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{12}{19}p+1x+1.\frac{12}{19}& \text{Uitwerken } \\ & =px+\frac{12}{19}p+1x+\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-12}{16})(\frac{15}{11}-q)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{-q}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{15}{11}p-\frac{3}{4}q+\frac{3}{4}.\frac{15}{11}& \text{Uitwerken } \\ & =-pq+\frac{15}{11}p-\frac{3}{4}q+\frac{45}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-11}{7}+a)(p-\frac{-8}{4})& =(\color{red}{a}+\color{orange}{\frac{-11}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a-\frac{11}{7}p-\frac{11}{7}.2& \text{Uitwerken } \\ & =ap+2a-\frac{11}{7}p-\frac{22}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)