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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-4}{8})(q+\frac{15}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{4}p-\frac{1}{2}q-\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =pq+\frac{3}{4}p-\frac{1}{2}q-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{7}{14})(q+\frac{13}{10})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{10}a-\frac{1}{2}q-\frac{1}{2}.\frac{13}{10}& \text{Uitwerken } \\ & =aq+\frac{13}{10}a-\frac{1}{2}q-\frac{13}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-15}{2}-q)(q+\frac{-2}{11})& =(\color{red}{-q}+\color{orange}{\frac{-15}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{2}{11}q-\frac{15}{2}q+\frac{15}{2}.\frac{2}{11}& \text{Uitwerken } \\ & =-q^2+(\frac{2}{11}+(\frac{-15}{2}))q+(\frac{-30}{22}) & \text{Neem samen} \\ &=-q^2-\frac{161}{22}q+(\frac{-30}{22}) & \text{Maak de som} \\ &=-q^2-\frac{161}{22}q+(\frac{-15}{11}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(\frac{-15}{2}+p)(\frac{-9}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{-15}{2}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{4}p+\frac{15}{2}b+\frac{15}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-bp-\frac{3}{4}p+\frac{15}{2}b+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}((-18)-p)(a-\frac{-2}{18})& =(\color{red}{-p}+\color{orange}{(-18)}).(\color{green}{a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-18)} . \color{green}{(a)} + \color{orange}{(-18)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{9}p-18a-18.\frac{1}{9}& \text{Uitwerken } \\ & =-ap-\frac{1}{9}p-18a-\frac{18}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{9}p-18a-2 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-13}{19}+q)(b-\frac{-1}{6})& =(\color{red}{q}+\color{orange}{\frac{-13}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{6}q-\frac{13}{19}b-\frac{13}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =bq+\frac{1}{6}q-\frac{13}{19}b-\frac{13}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{8}+a)(p-\frac{-6}{13})& =(\color{red}{a}+\color{orange}{\frac{-11}{8}}).(\color{green}{p}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{13}a-\frac{11}{8}p-\frac{11}{8}.\frac{6}{13}& \text{Uitwerken } \\ & =ap+\frac{6}{13}a-\frac{11}{8}p-\frac{66}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{13}a-\frac{11}{8}p-\frac{33}{52} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-4}{12}+p)(b+\frac{-2}{12})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{6}p-\frac{1}{3}b+\frac{1}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =bp-\frac{1}{6}p-\frac{1}{3}b+\frac{1}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-2}{7})(\frac{1}{16}-a)& =(\color{red}{b}+\color{orange}{\frac{2}{7}}).(\color{green}{-a}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{2}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{16}b-\frac{2}{7}a+\frac{2}{7}.\frac{1}{16}& \text{Uitwerken } \\ & =-ab+\frac{1}{16}b-\frac{2}{7}a+\frac{2}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{16}b-\frac{2}{7}a+\frac{1}{56} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{13}+b)(q+\frac{-11}{17})& =(\color{red}{b}+\color{orange}{\frac{-4}{13}}).(\color{green}{q}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{17}b-\frac{4}{13}q+\frac{4}{13}.\frac{11}{17}& \text{Uitwerken } \\ & =bq-\frac{11}{17}b-\frac{4}{13}q+\frac{44}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+(-6))(\frac{-14}{2}+x)& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ax-7a-6x+6.7& \text{Uitwerken } \\ & =ax-7a-6x+42 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{-13}{8})(a+\frac{15}{19})& =(\color{red}{x}+\color{orange}{\frac{-13}{8}}).(\color{green}{a}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{19}x-\frac{13}{8}a-\frac{13}{8}.\frac{15}{19}& \text{Uitwerken } \\ & =ax+\frac{15}{19}x-\frac{13}{8}a-\frac{195}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)