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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{4}{15})(\frac{-10}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{4}{15}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{4}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}p-\frac{4}{15}q-\frac{4}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}p-\frac{4}{15}q-\frac{4}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{2}p-\frac{4}{15}q-\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{5}{16}-a)(x-\frac{-3}{18})& =(\color{red}{-a}+\color{orange}{\frac{5}{16}}).(\color{green}{x}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{5}{16})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{6}a+\frac{5}{16}x+\frac{5}{16}.\frac{1}{6}& \text{Uitwerken } \\ & =-ax-\frac{1}{6}a+\frac{5}{16}x+\frac{5}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{12}{2})(\frac{-5}{17}-q)& =(\color{red}{q}+\color{orange}{6}).(\color{green}{-q}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(6)} . \color{green}{(-q)} + \color{orange}{(6)} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{5}{17}q-6q-6.\frac{5}{17}& \text{Uitwerken } \\ & =-q^2+((\frac{-5}{17})+(-6))q-\frac{30}{17} & \text{Neem samen} \\ &=-q^2-\frac{107}{17}q-\frac{30}{17} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{13}+p)(\frac{18}{12}+b)& =(\color{red}{p}+\color{orange}{\frac{-10}{13}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{2}p-\frac{10}{13}b-\frac{10}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =bp+\frac{3}{2}p-\frac{10}{13}b-\frac{30}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{2}p-\frac{10}{13}b-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{20}{4}-x)(\frac{-18}{9}-q)& =(\color{red}{-x}+\color{orange}{5}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(-2)} + \color{orange}{(5)} . \color{green}{(-q)} + \color{orange}{(5)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx+2x-5q-5.2& \text{Uitwerken } \\ & =qx+2x-5q-10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-19}{11}-p)(\frac{-12}{12}+p)& =(\color{red}{-p}+\color{orange}{\frac{-19}{11}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp+1p-\frac{19}{11}p+\frac{19}{11}.1& \text{Uitwerken } \\ & =-p^2+(1+(\frac{-19}{11}))p+(\frac{-19}{11}) & \text{Neem samen} \\ &=-p^2-\frac{8}{11}p+(\frac{-19}{11}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}((-14)-p)(p-\frac{6}{18})& =(\color{red}{-p}+\color{orange}{(-14)}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-14)} . \color{green}{(p)} + \color{orange}{(-14)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{3}p-14p+14.\frac{1}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{3}+(-14))p+(\frac{-14}{3}) & \text{Neem samen} \\ &=-p^2-\frac{41}{3}p+(\frac{-14}{3}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x-\frac{-12}{10})(\frac{9}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{-b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{17}x-\frac{6}{5}b+\frac{6}{5}.\frac{9}{17}& \text{Uitwerken } \\ & =-bx+\frac{9}{17}x-\frac{6}{5}b+\frac{54}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{20}+q)(q-\frac{11}{16})& =(\color{red}{q}+\color{orange}{\frac{-13}{20}}).(\color{green}{q}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{16}q-\frac{13}{20}q+\frac{13}{20}.\frac{11}{16}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{16})+(\frac{-13}{20}))q+\frac{143}{320} & \text{Neem samen} \\ &=q^2-\frac{107}{80}q+\frac{143}{320} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(b-\frac{3}{16})(\frac{17}{2}+x)& =(\color{red}{b}+\color{orange}{\frac{-3}{16}}).(\color{green}{x}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{2}b-\frac{3}{16}x-\frac{3}{16}.\frac{17}{2}& \text{Uitwerken } \\ & =bx+\frac{17}{2}b-\frac{3}{16}x-\frac{51}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b-\frac{4}{17})(\frac{14}{18}+a)& =(\color{red}{b}+\color{orange}{\frac{-4}{17}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{9}b-\frac{4}{17}a-\frac{4}{17}.\frac{7}{9}& \text{Uitwerken } \\ & =ab+\frac{7}{9}b-\frac{4}{17}a-\frac{28}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{2}{20})(q-\frac{-20}{5})& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4p+\frac{1}{10}q+\frac{1}{10}.4& \text{Uitwerken } \\ & =pq+4p+\frac{1}{10}q+\frac{4}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+4p+\frac{1}{10}q+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)