Ejercicio 72 – Solucionario Baldor

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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES

Hallar, por simple inspección, el cociente de:

$\frac{x^{6} + y^{6}}{x^{2} + y^{2}} = x^{4} - x^{2} y^{2} + y^{4}$
$\frac{a^{8} - b^{8}}{a^{2} + b^{2}} = a^{6} - a^{4} b^{2} + a^{2} b^{4} - b^{6}$
$\frac{m^{10} - n^{10}}{m^{2} - n^{2}} = m^{8} + m^{6} n^{2} + m^{4} n^{4} + m^{2} n^{6} + n^{8}$
$\frac{a^{12} - b^{12}}{a^{3} + b^{3}} = a^{9} - a^{6} b^{3} + a^{3} b^{6} - b^{9}$
$\frac{a^{12} - x^{12}}{a^{3} - x^{3}} = a^{9} + a^{6} x^{3} + a^{3} x^{6} + x^{9}$
$\frac{x^{15} + y^{15}}{x^{3} + y^{3}} = x^{12} - x^{9} y^{3} + x^{6} y^{6} - x^{3} y^{9} + y^{12}$
$\frac{m^{12} + 1}{m^{4} + 1} = m^{8} - m^{4} + 1$
$\frac{m^{16} - n^{16}}{m^{4} - n^{4}} = m^{12} + m^{8} n^{4} + m^{4} n^{8} + n^{12}$
$\frac{a^{18} - b^{18}}{a^{3} + b^{3}} = a^{15} - a^{12} b^{3} + a^{9} b^{6} - a^{6} b^{9} + a^{3} b^{12} - b^{15}$
$\frac{x^{20} - y^{20}}{x^{5} + y^{5}} = x^{15} - x^{10} y^{5} + x^{5} y^{10} - y^{15}$
$\frac{m^{21} + n^{21}}{m^{3} + n^{3}} = m^{18} - m^{15} n^{3} + m^{12} n^{6} - m^{9} n^{9} + m^{6} n^{12} - m^{3} n^{15} + n^{18}$
$\frac{x^{24} - 1}{x^{6} - 1} = x^{18} + x^{12} + x^{6} + 1$
$\frac{a^{25} + b^{25}}{a^{5} + b^{5}} = a^{20} - a^{15} b^{5} + a^{10} b^{10} - a^{5} b^{15} + b^{20}$
$\frac{a^{30} - m^{30}}{a^{6} - m^{6}} = a^{24} + a^{18} m^{6} + a^{12} m^{12} + a^{6} m^{18} + m^{24}$