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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{2}{13})(q+\frac{-14}{17})& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{q}+\color{blue}{\frac{-14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{17})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-14}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{14}{17}p-\frac{2}{13}q+\frac{2}{13}.\frac{14}{17}& \text{Uitwerken } \\ & =pq-\frac{14}{17}p-\frac{2}{13}q+\frac{28}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p+\frac{7}{2})(\frac{-15}{7}-a)& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{-a}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{15}{7}p-\frac{7}{2}a-\frac{7}{2}.\frac{15}{7}& \text{Uitwerken } \\ & =-ap-\frac{15}{7}p-\frac{7}{2}a-\frac{105}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{15}{7}p-\frac{7}{2}a-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p+\frac{4}{12})(b-\frac{2}{18})& =(\color{red}{p}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{9}p+\frac{1}{3}b-\frac{1}{3}.\frac{1}{9}& \text{Uitwerken } \\ & =bp-\frac{1}{9}p+\frac{1}{3}b-\frac{1}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{8}{16})(q-\frac{10}{8})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{4}q+\frac{1}{2}q-\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{4})+\frac{1}{2})q-(\frac{-5}{8}) & \text{Neem samen} \\ &=q^2-\frac{3}{4}q-(\frac{-5}{8}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(a-\frac{-11}{10})(b-\frac{-3}{11})& =(\color{red}{a}+\color{orange}{\frac{11}{10}}).(\color{green}{b}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{11}{10})} . \color{green}{(b)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{11}a+\frac{11}{10}b+\frac{11}{10}.\frac{3}{11}& \text{Uitwerken } \\ & =ab+\frac{3}{11}a+\frac{11}{10}b+\frac{33}{110} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{11}a+\frac{11}{10}b+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p-\frac{-3}{20})(a+\frac{-14}{19})& =(\color{red}{p}+\color{orange}{\frac{3}{20}}).(\color{green}{a}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{3}{20})} . \color{green}{(a)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{19}p+\frac{3}{20}a-\frac{3}{20}.\frac{14}{19}& \text{Uitwerken } \\ & =ap-\frac{14}{19}p+\frac{3}{20}a-\frac{42}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{14}{19}p+\frac{3}{20}a-\frac{21}{190} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{18}{4}-b)(q-\frac{4}{9})& =(\color{red}{-b}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{9}b+\frac{9}{2}q-\frac{9}{2}.\frac{4}{9}& \text{Uitwerken } \\ & =-bq+\frac{4}{9}b+\frac{9}{2}q-\frac{36}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{4}{9}b+\frac{9}{2}q-2 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{7}-a)(p-\frac{-9}{13})& =(\color{red}{-a}+\color{orange}{\frac{-18}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{13}a-\frac{18}{7}p-\frac{18}{7}.\frac{9}{13}& \text{Uitwerken } \\ & =-ap-\frac{9}{13}a-\frac{18}{7}p-\frac{162}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{9}+q)(\frac{-14}{9}-x)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{14}{9}q+2x+2.\frac{14}{9}& \text{Uitwerken } \\ & =-qx-\frac{14}{9}q+2x+\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-\frac{-20}{16})(\frac{1}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{-q}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{14}a-\frac{5}{4}q+\frac{5}{4}.\frac{1}{14}& \text{Uitwerken } \\ & =-aq+\frac{1}{14}a-\frac{5}{4}q+\frac{5}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}((-6)+b)(a+\frac{14}{20})& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{10}b-6a-6.\frac{7}{10}& \text{Uitwerken } \\ & =ab+\frac{7}{10}b-6a-\frac{42}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{7}{10}b-6a-\frac{21}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-13}{14}+a)(\frac{-7}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{-13}{14}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1a+\frac{13}{14}q+\frac{13}{14}.1& \text{Uitwerken } \\ & =-aq-1a+\frac{13}{14}q+\frac{13}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)