Ejercicio 206 – Solucionario Baldor

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DESCARGA

CAPITULO XXVIII

Problemas sobre ecuaciones simultaneas

Ejercicio 206

Desarrollar:

$\begin{matrix} {(a^{5} + 7 b^{4})}^{2} & = {(a^{5})}^{2} + 2 (a^{5}) (7 b^{4}) + {(7 b^{4})}^{2} \\ = a^{10} + 14 a^{5} b^{4} + 49 b^{8} \end{matrix}$
$\begin{matrix} {(3 x^{4} - 5 x y^{3})}^{2} & = {(3 x^{4})}^{2} - 2 (3 x^{4}) (5 x y^{3}) + {(- 5 x y^{3})}^{2} \\ = 9 x^{8} - 30 x^{5} y^{3} + 25 x^{2} y^{6} \end{matrix}$
$\begin{matrix} {(a^{2} b^{3} - a^{5})}^{2} & = {(a^{2} b^{3})}^{2} - 2 (a^{2} b^{3}) (a^{5}) + {(- a^{5})}^{2} \\ = a^{4} b^{6} - 2 a^{7} b^{3} + a^{10} \end{matrix}$
$\begin{matrix} {(7 x^{5} - 8 x^{3} y^{4})}^{2} & = {(7 x^{5})}^{2} - 2 (7 x^{5}) (8 x^{3} y^{4}) + {(- 8 x^{3} y^{4})}^{2} \\ = 49 x^{10} - 112 x^{8} y^{4} + 64 x^{6} y^{8} \end{matrix}$
$\begin{matrix} {(9 a b^{2} + 5 a^{2} b^{3})}^{2} & = {(9 a b^{2})}^{2} + 2 (9 a b^{2}) (5 a^{2} b^{3}) + {(5 a^{2} b^{3})}^{2} \\ = 81 a^{2} b^{4} + 90 a^{3} b^{5} + 25 a^{4} b^{6} \end{matrix}$
$\begin{matrix} {(3 x^{2} y^{3} - 7 x^{3} y^{2})}^{2} & = {(3 x^{2} y^{3})}^{2} - 2 (3 x^{2} y^{3}) (7 x^{3} y^{2}) + {(- 7 x^{3} y^{2})}^{2} \\ = 9 x^{4} y^{6} - 42 x^{5} y^{5} + 49 x^{6} y^{4} \end{matrix}$
$\begin{matrix} {(x y - a^{2} b^{2})}^{2} & = {(x y)}^{2} - 2 x y a^{2} b^{2} + {(- a^{2} b^{2})}^{2} \\ = x^{2} y^{2} - 2 x y a^{2} b^{2} + a^{4} b^{4} \end{matrix}$
$\begin{matrix} {(\frac{1}{2} x + \frac{2}{3} y)}^{2} & = {(\frac{1}{2} x)}^{2} + 2 (\frac{1}{2} x) (\frac{2}{3} y) + {(\frac{2}{3} y)}^{2} \\ = \frac{1}{4} x^{2} + \frac{2}{3} x y + \frac{4}{9} y^{2} \end{matrix}$
$\begin{matrix} {(\frac{3}{4} a^{2} - \frac{2}{5} b^{2})}^{2} & = {(\frac{3}{4} a^{2})}^{2} - 2 (\frac{3}{4} a^{2}) (\frac{2}{5} b^{2}) + {(- \frac{2}{5} b^{2})}^{2} \\ = \frac{9}{16} a^{4} - \frac{3}{5} a^{2} b^{2} + \frac{4}{25} b^{4} \end{matrix}$
$\begin{matrix} {(\frac{5}{6} x^{3} + \frac{3}{5} x y^{2})}^{2} & = {(\frac{5}{6} x^{3})}^{2} + 2 (\frac{5}{6} x^{3}) (\frac{3}{5} x y^{2}) + {(\frac{3}{5} x y^{2})}^{2} \\ = \frac{25}{36} x^{6} + x^{4} y^{2} + \frac{9}{25} x^{2} y^{4} \end{matrix}$
$\begin{matrix} {(\frac{1}{9} a^{5} - \frac{3}{7} a^{3} b^{7})}^{2} & = {(\frac{1}{9} a^{5})}^{2} - 2 (\frac{1}{} a^{5}) (\frac{3}{7} a^{3} b^{7}) + {(- \frac{3}{7} a^{3} b^{7})}^{2} \\ = \frac{1}{81} a^{10} - \frac{2}{21} a^{8} b^{7} + \frac{9}{49} a^{6} b^{14} \end{matrix}$
$\begin{matrix} {(\frac{2}{5} m^{4} - \frac{5}{4} n^{3})}^{2} & = {(\frac{2}{5} m^{4})}^{2} - 2 (\frac{2}{5} m^{4}) (\frac{5}{4} n^{3}) + {(- \frac{5}{4} n^{3})}^{2} \\ = \frac{4}{25} m^{8} - m^{4} n^{3} + \frac{25}{16} n^{6} \end{matrix}$
$\begin{matrix} {(\frac{x}{3} + \frac{y^{2}}{4})}^{2} & = {(\frac{x}{3})}^{2} + 2 (\frac{x}{3}) (\frac{y^{2}}{}) + {(\frac{y^{2}}{4})}^{2} \\ = \frac{x^{2}}{9} + \frac{x y^{2}}{6} + \frac{y^{4}}{16} \end{matrix}$
$\begin{matrix} {(\frac{2 x}{3} - \frac{3 y}{5})}^{2} & = {(\frac{2 x}{3})}^{2} + 2 (\frac{2 x}{3}) (\frac{3 y}{5}) + {(- \frac{3 y}{5})}^{2} \\ = \frac{4 x^{2}}{9} - \frac{4 x y}{5} + \frac{9 y^{2}}{25} \end{matrix}$
$\begin{matrix} {(\frac{a^{3}}{8} + \frac{4 a^{2}}{7 b})}^{2} & = {(\frac{a^{3}}{8})}^{2} + 2 (\frac{a^{3}}{8}) (\frac{4 a^{2}}{7 b}) + {(\frac{4 a^{2}}{7 b})}^{2} \\ = \frac{a^{6}}{64} + \frac{a^{5}}{7 b} + \frac{16 a^{4}}{49 b^{2}} \end{matrix}$
$\begin{matrix} {(\frac{3}{2 x} - \frac{2 x^{4}}{3})}^{2} & = {(\frac{3}{2 x})}^{2} - 2 (\frac{3}{2 x}) (\frac{2 x^{}}{3}) + {(- \frac{2 x^{4}}{3})}^{2} \\ = \frac{9}{4 x^{2}} - 2 x^{3} + \frac{4 x^{8}}{9} \end{matrix}$
$\begin{matrix} {(\frac{5 x^{7}}{6 y^{4}} - \frac{3 y^{6}}{10 x^{2}})}^{2} & = {(\frac{5 x^{7}}{6 y^{4}})}^{2} - 2 (\frac{5 x^{}}{y^{4}}) (\frac{3 y^{}}{10 x^{2}}) + {(- \frac{3 y^{6}}{10 x^{2}})}^{2} \\ = \frac{25 x^{14}}{36 y^{8}} - \frac{x^{5} y^{2}}{2} + \frac{9 y^{12}}{100 x^{4}} \end{matrix}$
$\begin{matrix} {(\frac{3}{8} a^{6} - \frac{4 a^{2}}{9 b^{5}})}^{2} & = {(\frac{3}{8} a^{6})}^{2} - 2 (\frac{3}{8} a^{6}) (\frac{4 a^{2}}{b^{5}}) + {(- \frac{4 a^{2}}{9 b^{5}})}^{2} \\ = \frac{9}{64} a^{12} - \frac{a^{8}}{3 b^{5}} + \frac{16 a^{4}}{81 b^{10}} \end{matrix}$