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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{1}{9}-p)(\frac{8}{4}-x)& =(\color{red}{-p}+\color{orange}{\frac{1}{9}}).(\color{green}{-x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-\frac{1}{9}x+\frac{1}{9}.2& \text{Uitwerken } \\ & =px-2p-\frac{1}{9}x+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{11}-x)(\frac{-6}{20}+x)& =(\color{red}{-x}+\color{orange}{\frac{16}{11}}).(\color{green}{x}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{10}x+\frac{16}{11}x-\frac{16}{11}.\frac{3}{10}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{10}+\frac{16}{11})x-\frac{48}{110} & \text{Neem samen} \\ &=-x^2+\frac{193}{110}x-\frac{48}{110} & \text{Maak de som} \\ &=-x^2+\frac{193}{110}x-\frac{24}{55} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
3. \(\begin{align}(\frac{-11}{10}+b)(p+\frac{13}{4})& =(\color{red}{b}+\color{orange}{\frac{-11}{10}}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{4}b-\frac{11}{10}p-\frac{11}{10}.\frac{13}{4}& \text{Uitwerken } \\ & =bp+\frac{13}{4}b-\frac{11}{10}p-\frac{143}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{12}-x)(b+\frac{13}{19})& =(\color{red}{-x}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{19}x-\frac{1}{6}b-\frac{1}{6}.\frac{13}{19}& \text{Uitwerken } \\ & =-bx-\frac{13}{19}x-\frac{1}{6}b-\frac{13}{114} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{13}{20}-x)(p+\frac{-2}{11})& =(\color{red}{-x}+\color{orange}{\frac{13}{20}}).(\color{green}{p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{11}x+\frac{13}{20}p-\frac{13}{20}.\frac{2}{11}& \text{Uitwerken } \\ & =-px+\frac{2}{11}x+\frac{13}{20}p-\frac{26}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{11}x+\frac{13}{20}p-\frac{13}{110} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p+\frac{6}{5})((-11)-a)& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{-a}+\color{blue}{(-11)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-11)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -ap-11p-\frac{6}{5}a-\frac{6}{5}.11& \text{Uitwerken } \\ & =-ap-11p-\frac{6}{5}a-\frac{66}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{14}{20}-x)(b-\frac{16}{17})& =(\color{red}{-x}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{16}{17}x+\frac{7}{10}b-\frac{7}{10}.\frac{16}{17}& \text{Uitwerken } \\ & =-bx+\frac{16}{17}x+\frac{7}{10}b-\frac{112}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{16}{17}x+\frac{7}{10}b-\frac{56}{85} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-\frac{-18}{3})(\frac{-9}{18}-b)& =(\color{red}{a}+\color{orange}{6}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(6)} . \color{green}{(-b)} + \color{orange}{(6)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a-6b-6.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a-6b-\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{1}{2}a-6b-3 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{10}{15}+q)(\frac{-9}{9}-a)& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1q-\frac{2}{3}a-\frac{2}{3}.1& \text{Uitwerken } \\ & =-aq-1q-\frac{2}{3}a-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{-18}{4})(\frac{9}{20}-p)& =(\color{red}{b}+\color{orange}{\frac{9}{2}}).(\color{green}{-p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{9}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{20}b-\frac{9}{2}p+\frac{9}{2}.\frac{9}{20}& \text{Uitwerken } \\ & =-bp+\frac{9}{20}b-\frac{9}{2}p+\frac{81}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{14}{12})(\frac{-17}{5}-p)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{-p}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{5}a+\frac{7}{6}p+\frac{7}{6}.\frac{17}{5}& \text{Uitwerken } \\ & =-ap-\frac{17}{5}a+\frac{7}{6}p+\frac{119}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{10}{17}-a)(\frac{-16}{4}+p)& =(\color{red}{-a}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-4)} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ap+4a+\frac{10}{17}p-\frac{10}{17}.4& \text{Uitwerken } \\ & =-ap+4a+\frac{10}{17}p-\frac{40}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)