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CAPITULO XXVIII

Problemas sobre ecuaciones simultaneas

Ejercicio 212

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3° término de ${(x - y)}^{5}$
$\begin{matrix} S e a : \\ n = 5 \\ r = 3 \\ t_{3} & = \frac{5 \times}{1 \times 2} x^{5 - (3 - 1)} y^{3 - 1} \\ t_{3} & = 10 x^{3} y^{2} \end{matrix}$
4° término de ${(a - 4 b)}^{7}$
$\begin{matrix} S e a : \\ n = 7 \\ r = 4 \\ t_{4} & = \frac{7 \times 6 \times 5}{1 \times 2 \times 3} a^{7 - (4 - 1)} {(- 4 b)}^{4 - 1} \\ t_{4} & = 35 a^{4} {(- 4 b)}^{3} \\ t_{4} & = - 2240 a^{4} b^{3} \end{matrix}$
5° término de ${(1 + x)}^{11}$
$\begin{matrix} S e a : \\ n = 11 \\ r = 5 \\ t_{5} & = \frac{11 \times 10 \times \times 8}{1 \times 2 \times 3 \times 4} 1^{11 - (5 - 1)} {(x)}^{5 - 1} \\ t_{5} & = 330 x^{4} \end{matrix}$
4° término de ${(3 x - 2 y)}^{6}$
$\begin{matrix} S e a : \\ n = 6 \\ r = 4 \\ t_{4} & = \frac{6 \times 5 \times 4}{1 \times 2 \times 3} {(3 x)}^{6 - (4 - 1)} {(- 2 y)}^{4 - 1} \\ t_{4} & = 20 (27 x^{3}) (- 8 y^{3}) \\ t_{4} & = - 4320 x^{3} y^{3} \end{matrix}$
5° término de ${(a^{2} - 2 b)}^{9}$
$\begin{matrix} S e a : \\ n = 9 \\ r = 5 \\ t_{5} & = \frac{9 \times 8 \times 7 \times}{1 \times 2 \times 3 \times 4} {(a^{2})}^{9 - (5 - 1)} {(- 2 b)}^{5 - 1} \\ t_{5} & = 126 (a^{10}) (16 b^{4}) \\ t_{5} & = 2016 a^{10} b^{4} \end{matrix}$
6° término de ${(2 a - \frac{b}{2})}^{8}$
$\begin{matrix} S e a : \\ n = 8 \\ r = 6 \\ t_{6} & = \frac{8 \times 7 \times 6 \times 5 \times 4}{1 \times 2 \times 3 \times 4 \times 5} {(2 a)}^{8 - (6 - 1)} {(- \frac{b}{2})}^{6 - 1} \\ t_{6} & = 56 (3 a^{3}) (- \frac{b^{5}}{32}) \\ t_{6} & = - 14 a^{3} b^{5} \end{matrix}$
7° término de ${(x^{2} - 2 y)}^{10}$
$\begin{matrix} S e a : \\ n = 10 \\ r = 7 \\ t_{7} & = \frac{10 \times \times 8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4 \times 5 \times 6} {(x^{2})}^{10 - (7 - 1)} {(- 2 y)}^{7 - 1} \\ t_{7} & = 210 (x^{8}) (64 y^{6}) \\ t_{7} & = 13440 x^{8} y^{6} \end{matrix}$
8° término de ${(x - y^{2})}^{11}$
$\begin{matrix} S e a : \\ n = 11 \\ r = 8 \\ t_{8} & = \frac{11 \times 10 \times \times 8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7} {(x)}^{11 - (8 - 1)} {(- y^{2})}^{8 - 1} \\ t_{8} & = 330 x^{4} (- y^{14}) \\ t_{8} & = - 330 x^{4} y^{14} \end{matrix}$
10° término de ${(a^{2} + b)}^{15}$
$\begin{matrix} S e a : \\ n = 15 \\ r = 10 \\ t_{10} & = \frac{15 \times \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7}{1 \times 2 \times 3 \times 4 \times 5 \times \times 7 \times 8 \times 9} {(a^{2})}^{15 - (10 - 1)} {(b)}^{10 - 1} \\ t_{10} & = 5005 a^{12} b^{9} \end{matrix}$
9° término de ${(1 - x^{2})}^{12}$
$\begin{matrix} S e a : \\ n = 12 \\ r = 9 \\ t_{9} & = \frac{12 \times 11 \times \times 9 \times 8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8} {(1)}^{12 - (9 - 1)} {(- x^{2})}^{9 - 1} \\ t_{9} & = 495 x^{16} \end{matrix}$
El penúltimo término de ${(2 a - b^{2})}^{6}$
$\begin{matrix} S e a : \\ n = 6 \\ r = 6 \\ t_{6} & = \frac{6 \times 5 \times 4 \times 3 \times 2}{1 \times 2 \times 3 \times 4 \times 5} {(2 a)}^{6 - (6 - 1)} {(- b^{2})}^{6 - 1} \\ t_{6} & = 6 (2 a) (- b^{10}) \\ t_{6} & = - 12 a b^{10} \end{matrix}$
El término del medio de ${(3 x^{2} - y^{2})}^{8}$
$\begin{matrix} S e a : \\ n = 8 \\ r = 5 \\ t_{5} & = \frac{\times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4} {(3 x^{2})}^{8 - (5 - 1)} {(- y^{2})}^{5 - 1} \\ t_{5} & = 70 (81 x^{8}) (y^{8}) \\ t_{5} & = 5670 x^{8} y^{8} \end{matrix}$