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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{12}{9})(\frac{-4}{3}+q)& =(\color{red}{q}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{3}q-\frac{4}{3}q+\frac{4}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{3})+(\frac{-4}{3}))q+\frac{16}{9} & \text{Neem samen} \\ &=q^2-\frac{8}{3}q+\frac{16}{9} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(6-a)(\frac{18}{11}-b)& =(\color{red}{-a}+\color{orange}{6}).(\color{green}{-b}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(6)} . \color{green}{(-b)} + \color{orange}{(6)} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{18}{11}a-6b+6.\frac{18}{11}& \text{Uitwerken } \\ & =ab-\frac{18}{11}a-6b+\frac{108}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{-11}{15})(b-\frac{19}{5})& =(\color{red}{q}+\color{orange}{\frac{11}{15}}).(\color{green}{b}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{19}{5}q+\frac{11}{15}b-\frac{11}{15}.\frac{19}{5}& \text{Uitwerken } \\ & =bq-\frac{19}{5}q+\frac{11}{15}b-\frac{209}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+15)(q-\frac{17}{7})& =(\color{red}{a}+\color{orange}{15}).(\color{green}{q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(15)} . \color{green}{(q)} + \color{orange}{(15)} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{7}a+15q-15.\frac{17}{7}& \text{Uitwerken } \\ & =aq-\frac{17}{7}a+15q-\frac{255}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{3}-p)(\frac{18}{2}-b)& =(\color{red}{-p}+\color{orange}{\frac{-10}{3}}).(\color{green}{-b}+\color{blue}{9})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(9)} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = bp-9p+\frac{10}{3}b-\frac{10}{3}.9& \text{Uitwerken } \\ & =bp-9p+\frac{10}{3}b-\frac{90}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-9p+\frac{10}{3}b-30 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q-\frac{-16}{16})(\frac{4}{10}-q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{2}{5}q-1q+1.\frac{2}{5}& \text{Uitwerken } \\ & =-q^2+(\frac{2}{5}+(-1))q+(\frac{-2}{5}) & \text{Neem samen} \\ &=-q^2-\frac{3}{5}q+(\frac{-2}{5}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{9}{20}-a)(\frac{-16}{5}-a)& =(\color{red}{-a}+\color{orange}{\frac{9}{20}}).(\color{green}{-a}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{9}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{16}{5}a-\frac{9}{20}a-\frac{9}{20}.\frac{16}{5}& \text{Uitwerken } \\ & =a^2+(\frac{16}{5}+(\frac{-9}{20}))a-(\frac{-144}{100}) & \text{Neem samen} \\ &=a^2+\frac{55}{20}a-(\frac{-144}{100}) & \text{Maak de som} \\ &=a^2+\frac{11}{4}a+\frac{36}{25} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(q+\frac{5}{13})(\frac{-15}{17}+x)& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{x}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{15}{17}q+\frac{5}{13}x-\frac{5}{13}.\frac{15}{17}& \text{Uitwerken } \\ & =qx-\frac{15}{17}q+\frac{5}{13}x-\frac{75}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-14}{19})(b+\frac{-10}{4})& =(\color{red}{x}+\color{orange}{\frac{-14}{19}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{2}x-\frac{14}{19}b+\frac{14}{19}.\frac{5}{2}& \text{Uitwerken } \\ & =bx-\frac{5}{2}x-\frac{14}{19}b+\frac{70}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{5}{2}x-\frac{14}{19}b+\frac{35}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(x+\frac{-10}{8})(\frac{-12}{8}+q)& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{2}x-\frac{5}{4}q+\frac{5}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =qx-\frac{3}{2}x-\frac{5}{4}q+\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-17}{15}-b)(q-(-9))& =(\color{red}{-b}+\color{orange}{\frac{-17}{15}}).(\color{green}{q}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(9)} + \color{orange}{(\frac{-17}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -bq-9b-\frac{17}{15}q-\frac{17}{15}.9& \text{Uitwerken } \\ & =-bq-9b-\frac{17}{15}q-\frac{153}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-9b-\frac{17}{15}q-\frac{51}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{11}+a)((-10)-q)& =(\color{red}{a}+\color{orange}{\frac{-20}{11}}).(\color{green}{-q}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-10)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -aq-10a+\frac{20}{11}q+\frac{20}{11}.10& \text{Uitwerken } \\ & =-aq-10a+\frac{20}{11}q+\frac{200}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)