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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{19}+q)(\frac{-8}{15}-x)& =(\color{red}{q}+\color{orange}{\frac{-5}{19}}).(\color{green}{-x}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{15}q+\frac{5}{19}x+\frac{5}{19}.\frac{8}{15}& \text{Uitwerken } \\ & =-qx-\frac{8}{15}q+\frac{5}{19}x+\frac{40}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{8}{15}q+\frac{5}{19}x+\frac{8}{57} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p+\frac{-8}{20})(b+\frac{5}{7})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{7}p-\frac{2}{5}b-\frac{2}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =bp+\frac{5}{7}p-\frac{2}{5}b-\frac{10}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{7}p-\frac{2}{5}b-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{11}{5})(q+\frac{-3}{7})& =(\color{red}{b}+\color{orange}{\frac{-11}{5}}).(\color{green}{q}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{7}b-\frac{11}{5}q+\frac{11}{5}.\frac{3}{7}& \text{Uitwerken } \\ & =bq-\frac{3}{7}b-\frac{11}{5}q+\frac{33}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{16}{11}+b)(\frac{15}{3}-a)& =(\color{red}{b}+\color{orange}{\frac{16}{11}}).(\color{green}{-a}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{16}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -ab+5b-\frac{16}{11}a+\frac{16}{11}.5& \text{Uitwerken } \\ & =-ab+5b-\frac{16}{11}a+\frac{80}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-(-1))(\frac{8}{5}+a)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{5}q+1a+1.\frac{8}{5}& \text{Uitwerken } \\ & =aq+\frac{8}{5}q+1a+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-16}{12}+a)(p-\frac{-8}{4})& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a-\frac{4}{3}p-\frac{4}{3}.2& \text{Uitwerken } \\ & =ap+2a-\frac{4}{3}p-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-15}{16}+x)(b-\frac{5}{16})& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{b}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{16}x-\frac{15}{16}b+\frac{15}{16}.\frac{5}{16}& \text{Uitwerken } \\ & =bx-\frac{5}{16}x-\frac{15}{16}b+\frac{75}{256} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x-\frac{-9}{16})(p+\frac{-13}{17})& =(\color{red}{x}+\color{orange}{\frac{9}{16}}).(\color{green}{p}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{9}{16})} . \color{green}{(p)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{17}x+\frac{9}{16}p-\frac{9}{16}.\frac{13}{17}& \text{Uitwerken } \\ & =px-\frac{13}{17}x+\frac{9}{16}p-\frac{117}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-5}{14})(a+\frac{11}{13})& =(\color{red}{a}+\color{orange}{\frac{5}{14}}).(\color{green}{a}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{5}{14})} . \color{green}{(a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{13}a+\frac{5}{14}a+\frac{5}{14}.\frac{11}{13}& \text{Uitwerken } \\ & =a^2+(\frac{11}{13}+\frac{5}{14})a+\frac{55}{182} & \text{Neem samen} \\ &=a^2+\frac{219}{182}a+\frac{55}{182} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p+\frac{-11}{20})(\frac{-8}{8}+p)& =(\color{red}{p}+\color{orange}{\frac{-11}{20}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p-\frac{11}{20}p+\frac{11}{20}.1& \text{Uitwerken } \\ & =p^2+((-1)+(\frac{-11}{20}))p+\frac{11}{20} & \text{Neem samen} \\ &=p^2-\frac{31}{20}p+\frac{11}{20} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{1}{17}+p)(\frac{-20}{3}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{17}}).(\color{green}{a}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{1}{17})} . \color{green}{(a)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{3}p+\frac{1}{17}a-\frac{1}{17}.\frac{20}{3}& \text{Uitwerken } \\ & =ap-\frac{20}{3}p+\frac{1}{17}a-\frac{20}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{12}{12})(\frac{-5}{15}-b)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{3}p+1b+1.\frac{1}{3}& \text{Uitwerken } \\ & =-bp-\frac{1}{3}p+1b+\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)