Question

разложить на множители 1)-x³+1/y³ 2)x³y³-1 3)-1/8-a³​

Answer 1

1)

$- {x}^{3} + \frac{1}{ {y}^{3} } = - ( {x}^{3} - \frac{1}{{y}^{3} }) = - (x - \frac{1}{y} )( {x}^{2} + \frac{x}{y} + \frac{1}{ {y}^{2} } )$

2)

${x}^{3} {y}^{3} - {1}^{3} = (xy - 1)( {(xy)}^{2} + xy \times 1 + {1}^{2} ) = (xy - 1)( {x}^{2} {y}^{2} + xy + 1)$

3)

$- \frac{1}{8} - {a}^{3} = \frac{1}{8} ( - 1 - 8 {a}^{3} ) = \frac{1}{8} ( - (1 + 8 {a}^{3} )) = \frac{1}{8} ( - (1 + 2a)(1 - 2a + 4 {a}^{2} )) = - \frac{1}{8} (1 + 2a)(1 - 2a + 4 {a}^{2} )$