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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{16}-x)(b-\frac{15}{16})& =(\color{red}{-x}+\color{orange}{\frac{-5}{8}}).(\color{green}{b}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{16}x-\frac{5}{8}b+\frac{5}{8}.\frac{15}{16}& \text{Uitwerken } \\ & =-bx+\frac{15}{16}x-\frac{5}{8}b+\frac{75}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{20}{11})(\frac{7}{8}+p)& =(\color{red}{b}+\color{orange}{\frac{-20}{11}}).(\color{green}{p}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-20}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{8}b-\frac{20}{11}p-\frac{20}{11}.\frac{7}{8}& \text{Uitwerken } \\ & =bp+\frac{7}{8}b-\frac{20}{11}p-\frac{140}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{8}b-\frac{20}{11}p-\frac{35}{22} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{15}{19})(\frac{18}{17}-a)& =(\color{red}{b}+\color{orange}{\frac{15}{19}}).(\color{green}{-a}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{15}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{18}{17}b-\frac{15}{19}a+\frac{15}{19}.\frac{18}{17}& \text{Uitwerken } \\ & =-ab+\frac{18}{17}b-\frac{15}{19}a+\frac{270}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{9}{20}-p)(p+\frac{-15}{2})& =(\color{red}{-p}+\color{orange}{\frac{9}{20}}).(\color{green}{p}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{2}p+\frac{9}{20}p-\frac{9}{20}.\frac{15}{2}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{2}+\frac{9}{20})p-\frac{135}{40} & \text{Neem samen} \\ &=-p^2+\frac{159}{20}p-\frac{135}{40} & \text{Maak de som} \\ &=-p^2+\frac{159}{20}p-\frac{27}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(x+\frac{10}{5})(\frac{10}{6}-b)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{3}x-2b+2.\frac{5}{3}& \text{Uitwerken } \\ & =-bx+\frac{5}{3}x-2b+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{18}-x)(q+(-13))& =(\color{red}{-x}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{(-13)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-13)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -qx+13x-\frac{1}{9}q+\frac{1}{9}.13& \text{Uitwerken } \\ & =-qx+13x-\frac{1}{9}q+\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{6}{15}-b)(\frac{15}{5}-q)& =(\color{red}{-b}+\color{orange}{\frac{2}{5}}).(\color{green}{-q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(3)} + \color{orange}{(\frac{2}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bq-3b-\frac{2}{5}q+\frac{2}{5}.3& \text{Uitwerken } \\ & =bq-3b-\frac{2}{5}q+\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{2}{17})(a+\frac{-12}{2})& =(\color{red}{b}+\color{orange}{\frac{2}{17}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ab-6b+\frac{2}{17}a-\frac{2}{17}.6& \text{Uitwerken } \\ & =ab-6b+\frac{2}{17}a-\frac{12}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{9}-q)(\frac{-13}{5}+x)& =(\color{red}{-q}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{5}q-\frac{1}{3}x+\frac{1}{3}.\frac{13}{5}& \text{Uitwerken } \\ & =-qx+\frac{13}{5}q-\frac{1}{3}x+\frac{13}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{14}{11})(\frac{-3}{20}-a)& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{-a}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{3}{20}q+\frac{14}{11}a+\frac{14}{11}.\frac{3}{20}& \text{Uitwerken } \\ & =-aq-\frac{3}{20}q+\frac{14}{11}a+\frac{42}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{3}{20}q+\frac{14}{11}a+\frac{21}{110} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{14}{4})(q-\frac{-7}{8})& =(\color{red}{x}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{8}x-\frac{7}{2}q-\frac{7}{2}.\frac{7}{8}& \text{Uitwerken } \\ & =qx+\frac{7}{8}x-\frac{7}{2}q-\frac{49}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{20}{8})(q+(-13))& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-13)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = bq-13b-\frac{5}{2}q+\frac{5}{2}.13& \text{Uitwerken } \\ & =bq-13b-\frac{5}{2}q+\frac{65}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)