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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-7}{15}+b)(\frac{-19}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{-x}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{19}{6}b+\frac{7}{15}x+\frac{7}{15}.\frac{19}{6}& \text{Uitwerken } \\ & =-bx-\frac{19}{6}b+\frac{7}{15}x+\frac{133}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{3}+p)(b+\frac{9}{5})& =(\color{red}{p}+\color{orange}{\frac{-19}{3}}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{5}p-\frac{19}{3}b-\frac{19}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =bp+\frac{9}{5}p-\frac{19}{3}b-\frac{171}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{5}p-\frac{19}{3}b-\frac{57}{5} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p-\frac{11}{6})(\frac{15}{2}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{6}}).(\color{green}{-b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{2}p+\frac{11}{6}b-\frac{11}{6}.\frac{15}{2}& \text{Uitwerken } \\ & =-bp+\frac{15}{2}p+\frac{11}{6}b-\frac{165}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{15}{2}p+\frac{11}{6}b-\frac{55}{4} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{-3}{7})(a+\frac{-16}{3})& =(\color{red}{p}+\color{orange}{\frac{-3}{7}}).(\color{green}{a}+\color{blue}{\frac{-16}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{3})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-16}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{3}p-\frac{3}{7}a+\frac{3}{7}.\frac{16}{3}& \text{Uitwerken } \\ & =ap-\frac{16}{3}p-\frac{3}{7}a+\frac{48}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{16}{3}p-\frac{3}{7}a+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{13}{14}-a)(\frac{1}{13}-b)& =(\color{red}{-a}+\color{orange}{\frac{13}{14}}).(\color{green}{-b}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{13}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{13}a-\frac{13}{14}b+\frac{13}{14}.\frac{1}{13}& \text{Uitwerken } \\ & =ab-\frac{1}{13}a-\frac{13}{14}b+\frac{13}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{13}a-\frac{13}{14}b+\frac{1}{14} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{-18}{6})(b+\frac{-5}{12})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{12}q-3b+3.\frac{5}{12}& \text{Uitwerken } \\ & =bq-\frac{5}{12}q-3b+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{12}q-3b+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a-\frac{1}{20})(\frac{19}{16}+a)& =(\color{red}{a}+\color{orange}{\frac{-1}{20}}).(\color{green}{a}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-1}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{16}a-\frac{1}{20}a-\frac{1}{20}.\frac{19}{16}& \text{Uitwerken } \\ & =a^2+(\frac{19}{16}+(\frac{-1}{20}))a-(\frac{-19}{320}) & \text{Neem samen} \\ &=a^2+\frac{91}{80}a-(\frac{-19}{320}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(b+\frac{-18}{11})(q-\frac{18}{7})& =(\color{red}{b}+\color{orange}{\frac{-18}{11}}).(\color{green}{q}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{7}b-\frac{18}{11}q+\frac{18}{11}.\frac{18}{7}& \text{Uitwerken } \\ & =bq-\frac{18}{7}b-\frac{18}{11}q+\frac{324}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-19}{4})(\frac{-3}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{-19}{4}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{19}{4}q+\frac{19}{4}.1& \text{Uitwerken } \\ & =pq-1p-\frac{19}{4}q+\frac{19}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{6}{17}+b)(b+\frac{8}{10})& =(\color{red}{b}+\color{orange}{\frac{6}{17}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{6}{17})} . \color{green}{(b)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{5}b+\frac{6}{17}b+\frac{6}{17}.\frac{4}{5}& \text{Uitwerken } \\ & =b^2+(\frac{4}{5}+\frac{6}{17})b+\frac{24}{85} & \text{Neem samen} \\ &=b^2+\frac{98}{85}b+\frac{24}{85} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{17}{9}-b)(\frac{-15}{13}+a)& =(\color{red}{-b}+\color{orange}{\frac{17}{9}}).(\color{green}{a}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{15}{13}b+\frac{17}{9}a-\frac{17}{9}.\frac{15}{13}& \text{Uitwerken } \\ & =-ab+\frac{15}{13}b+\frac{17}{9}a-\frac{255}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{15}{13}b+\frac{17}{9}a-\frac{85}{39} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}((-13)-x)(p+\frac{-15}{3})& =(\color{red}{-x}+\color{orange}{(-13)}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-5)} + \color{orange}{(-13)} . \color{green}{(p)} + \color{orange}{(-13)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -px+5x-13p+13.5& \text{Uitwerken } \\ & =-px+5x-13p+65 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)