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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-7}{17})(\frac{15}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{7}{17}}).(\color{green}{b}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{7}{17})} . \color{green}{(b)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{15}{13}p+\frac{7}{17}b+\frac{7}{17}.\frac{15}{13}& \text{Uitwerken } \\ & =bp+\frac{15}{13}p+\frac{7}{17}b+\frac{105}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{12}{5}+x)(b+\frac{-15}{14})& =(\color{red}{x}+\color{orange}{\frac{12}{5}}).(\color{green}{b}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{12}{5})} . \color{green}{(b)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{15}{14}x+\frac{12}{5}b-\frac{12}{5}.\frac{15}{14}& \text{Uitwerken } \\ & =bx-\frac{15}{14}x+\frac{12}{5}b-\frac{180}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{15}{14}x+\frac{12}{5}b-\frac{18}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p+\frac{-17}{8})(\frac{9}{4}+q)& =(\color{red}{p}+\color{orange}{\frac{-17}{8}}).(\color{green}{q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{4}p-\frac{17}{8}q-\frac{17}{8}.\frac{9}{4}& \text{Uitwerken } \\ & =pq+\frac{9}{4}p-\frac{17}{8}q-\frac{153}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-1}{2}+a)(b+\frac{4}{8})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-\frac{1}{2}b-\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-\frac{1}{2}b-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{8}+a)(\frac{-6}{6}-p)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a+\frac{3}{4}p+\frac{3}{4}.1& \text{Uitwerken } \\ & =-ap-1a+\frac{3}{4}p+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{7}{17}-p)(q+\frac{19}{2})& =(\color{red}{-p}+\color{orange}{\frac{7}{17}}).(\color{green}{q}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{2}p+\frac{7}{17}q+\frac{7}{17}.\frac{19}{2}& \text{Uitwerken } \\ & =-pq-\frac{19}{2}p+\frac{7}{17}q+\frac{133}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{-20}{7})(\frac{-7}{15}-p)& =(\color{red}{a}+\color{orange}{\frac{-20}{7}}).(\color{green}{-p}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{15}a+\frac{20}{7}p+\frac{20}{7}.\frac{7}{15}& \text{Uitwerken } \\ & =-ap-\frac{7}{15}a+\frac{20}{7}p+\frac{140}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{15}a+\frac{20}{7}p+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-9}{20}+q)(q-\frac{-6}{8})& =(\color{red}{q}+\color{orange}{\frac{-9}{20}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{4}q-\frac{9}{20}q-\frac{9}{20}.\frac{3}{4}& \text{Uitwerken } \\ & =q^2+(\frac{3}{4}+(\frac{-9}{20}))q-(\frac{-27}{80}) & \text{Neem samen} \\ &=q^2+\frac{6}{20}q-(\frac{-27}{80}) & \text{Maak de som} \\ &=q^2+\frac{3}{10}q+\frac{27}{80} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
9. \(\begin{align}(q+\frac{-6}{19})(\frac{8}{15}-p)& =(\color{red}{q}+\color{orange}{\frac{-6}{19}}).(\color{green}{-p}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{8}{15}q+\frac{6}{19}p-\frac{6}{19}.\frac{8}{15}& \text{Uitwerken } \\ & =-pq+\frac{8}{15}q+\frac{6}{19}p-\frac{48}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{8}{15}q+\frac{6}{19}p-\frac{16}{95} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{8}+b)(p-\frac{-17}{20})& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{p}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{20}b-\frac{3}{8}p-\frac{3}{8}.\frac{17}{20}& \text{Uitwerken } \\ & =bp+\frac{17}{20}b-\frac{3}{8}p-\frac{51}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-13}{2})(q-\frac{-12}{7})& =(\color{red}{x}+\color{orange}{\frac{-13}{2}}).(\color{green}{q}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{7}x-\frac{13}{2}q-\frac{13}{2}.\frac{12}{7}& \text{Uitwerken } \\ & =qx+\frac{12}{7}x-\frac{13}{2}q-\frac{156}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{7}x-\frac{13}{2}q-\frac{78}{7} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p+\frac{-16}{12})(x+\frac{-7}{11})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{11}p-\frac{4}{3}x+\frac{4}{3}.\frac{7}{11}& \text{Uitwerken } \\ & =px-\frac{7}{11}p-\frac{4}{3}x+\frac{28}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)