Ejercicio 103 – Solucionario Baldor

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CAPITULO X

Descomposición Factorial

Ejercicio 103

Descomponer en 2 factores:

$1 + a^{3} = (1 + a) (1 - a + a^{2})$
$1 - a^{3} = (1 - a) (1 + a + a^{2})$
$x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
$m^{3} - n^{3} = (m - n) (m^{2} + m n + n^{2})$
$a^{3} - 1 = (a - 1) (a^{2} + a + 1)$
$y^{3} + 1 = (y + 1) (y^{2} - y + 1)$
$y^{3} - 1 = (y - 1) (y^{2} + y + 1)$
$8 x^{3} - 1 = (2 x - 1) (4 x^{2} + 2 x + 1)$
$1 - 8 x^{3} = (1 - 2 x) (1 + 2 x + 4 x^{2})$
$x^{3} - 27 = (x - 3) (x^{2} + 3 x + 9)$
$a^{3} + 27 = (a + 3) (a^{2} - 3 a + 9)$
$8 x^{3} + y^{3} = (2 x + y) (4 x^{2} - 2 x y + y^{2})$
$27 a^{3} - b^{3} = (3 a - b) (9 a^{2} + 3 a b + b^{2})$
$64 + a^{6} = (4 + a^{2}) (16 - 4 a^{2} + a^{4})$
$a^{3} - 125 = (a - 5) (a^{2} + 5 a + 25)$
$1 - 216 m^{3} = (1 - 6 m) (1 + 6 m + 36 m^{2})$
$8 a^{3} + 27 b^{6} = (2 a + 3 b^{2}) (4 a^{2} - 6 a b^{2} + 9 b^{6})$
$x^{6} - b^{9} = (x^{2} - b^{3}) (x^{4} + x^{2} b^{3} + b^{3})$
$8 x^{3} - 27 y^{3} = (2 x - 3 y) (4 x^{2} + 6 x y + 9 y^{2})$
$1 + 343 n^{3} = (1 + 7 n) (1 - 7 n + 49 n^{2})$
$64 a^{3} - 729 = (4 a - 9) (16 a^{2} + 36 a + 81)$
$a^{3} b^{3} - x^{6} = (a b - x^{2}) (a^{2} b^{2} + a b x^{2} + x^{4})$
$512 + 27 a^{9} = (8 + 3 a^{3}) (64 - 24 a^{3} + 9 a^{6})$
$x^{6} - 8 y^{12} = (x^{2} - 2 y^{4}) (x^{4} + 2 x^{2} y^{4} + 4 y^{8})$
$1 + 729 x^{6} = (1 + 9 x^{2}) (1 - 9 x^{2} + 81 x^{4})$
$27 m^{3} + 64 n^{9} = (3 m + 4 n^{3}) (3 m^{2} - 12 m n^{3} + 16 n^{6})$
$343 x^{3} + 512 y^{6} = (7 x + 8 y^{2}) (49 x^{2} - 56 x y^{2} + 64 y^{4})$
$x^{3} y^{6} - 216 y^{9} = (x y^{2} - 6 y^{3}) (x^{2} y^{4} + 6 x y^{5} + 36 y^{6})$
$a^{3} b^{3} x^{3} + 1 = (a b x + 1) (a^{2} b^{2} x^{2} - a b x + 1)$
$x^{9} + y^{9} = (x^{3} + y^{3}) (x^{6} - x^{3} y^{3} + y^{6})$
$1000 x^{3} - 1 = (10 x - 1) (100 x^{2} + 10 x + 1)$
$a^{6} + 125 b^{12} = (a^{2} + 5 b^{4}) (a^{4} - 5 a^{2} b^{4} + 25 b^{8})$
$x^{12} + y^{12} = (x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + y^{8})$
$1 - 27 a^{3} b^{3} = (1 - 3 a b) (1 + 3 a b + 9 a^{2} b^{2})$
$8 x^{6} + 729 = (2 x^{2} + 9) (4 x^{4} - 18 x^{2} + 81)$
$a^{3} + 8 b^{12} = (a + 2 b^{4}) (a^{2} - 2 a b^{4} + 4 b^{8})$
$8 x^{9} - 125 y^{3} z^{6} = (2 x^{3} - 5 y z^{2}) (4 x^{6} + 10 x^{3} y z^{2} + 25 y^{2} z^{4})$
$27 m^{6} + 343 n^{9} = (3 m^{2} + 7 n^{3}) (9 m^{4} - 21 m^{2} n^{3} + 49 n^{6})$
$216 - x^{12} = (6 - x^{4}) (36 + 6 x^{4} + x^{8})$