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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-18}{9})(\frac{1}{15}+p)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{15}p-2p-2.\frac{1}{15}& \text{Uitwerken } \\ & =p^2+(\frac{1}{15}+(-2))p-(\frac{-2}{15}) & \text{Neem samen} \\ &=p^2-\frac{29}{15}p-(\frac{-2}{15}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(a+\frac{1}{3})((-2)+x)& =(\color{red}{a}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ax-2a+\frac{1}{3}x-\frac{1}{3}.2& \text{Uitwerken } \\ & =ax-2a+\frac{1}{3}x-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-18}{3}-a)(\frac{-10}{3}+x)& =(\color{red}{-a}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{10}{3}a-6x+6.\frac{10}{3}& \text{Uitwerken } \\ & =-ax+\frac{10}{3}a-6x+\frac{60}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{10}{3}a-6x+20 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}((-4)+p)(\frac{16}{6}+a)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{3}p-4a-4.\frac{8}{3}& \text{Uitwerken } \\ & =ap+\frac{8}{3}p-4a-\frac{32}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{-6}{16})(b-\frac{-12}{8})& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{2}b+\frac{3}{8}b+\frac{3}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+(\frac{3}{2}+\frac{3}{8})b+\frac{9}{16} & \text{Neem samen} \\ &=b^2+\frac{15}{8}b+\frac{9}{16} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b+\frac{-8}{6})(q+\frac{14}{9})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{14}{9}b-\frac{4}{3}q-\frac{4}{3}.\frac{14}{9}& \text{Uitwerken } \\ & =bq+\frac{14}{9}b-\frac{4}{3}q-\frac{56}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{18}{16})(x-\frac{-2}{11})& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{x}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{11}x+\frac{9}{8}x+\frac{9}{8}.\frac{2}{11}& \text{Uitwerken } \\ & =x^2+(\frac{2}{11}+\frac{9}{8})x+\frac{18}{88} & \text{Neem samen} \\ &=x^2+\frac{115}{88}x+\frac{18}{88} & \text{Maak de som} \\ &=x^2+\frac{115}{88}x+\frac{9}{44} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(b+\frac{-11}{3})(\frac{-13}{15}-a)& =(\color{red}{b}+\color{orange}{\frac{-11}{3}}).(\color{green}{-a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{15}b+\frac{11}{3}a+\frac{11}{3}.\frac{13}{15}& \text{Uitwerken } \\ & =-ab-\frac{13}{15}b+\frac{11}{3}a+\frac{143}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(16+a)(\frac{10}{5}+x)& =(\color{red}{a}+\color{orange}{16}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(16)} . \color{green}{(x)} + \color{orange}{(16)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a+16x+16.2& \text{Uitwerken } \\ & =ax+2a+16x+32 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-\frac{13}{17})(\frac{-5}{20}+x)& =(\color{red}{a}+\color{orange}{\frac{-13}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{4}a-\frac{13}{17}x+\frac{13}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =ax-\frac{1}{4}a-\frac{13}{17}x+\frac{13}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{8}{6}+p)(\frac{-16}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{4}{3}}).(\color{green}{-q}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{16}{5}p-\frac{4}{3}q-\frac{4}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =-pq-\frac{16}{5}p-\frac{4}{3}q-\frac{64}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-14}{12})(\frac{13}{12}-x)& =(\color{red}{q}+\color{orange}{\frac{-7}{6}}).(\color{green}{-x}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{12}q+\frac{7}{6}x-\frac{7}{6}.\frac{13}{12}& \text{Uitwerken } \\ & =-qx+\frac{13}{12}q+\frac{7}{6}x-\frac{91}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)