Question

Разложите на множители:
a) y³ - 2y² + 2y - 1
b) x³ - y³ - 5x(x^2 + xy + y^2)

Answer 1

$a)$

${y}^{3} - 2 {y}^{2} + 2y - 1$

$(y - 1) \times ( {y}^{2} + y + 1) - 2y \times (y - 1)$

$(y - 1) \times ( {y}^{2} + y + 1 - 2y)$

$(y - 1) \times ( {y}^{2} - y + 1)$

$b)$

${x}^{3} - {y}^{3} - 5x( {x}^{2} + xy + {y}^{2} )$

${x}^{3} - {y}^{3} - 5 {x}^{3} - 5 {x}^{2}y - 5x {y}^{2}$

$- 4 {x}^{3} - {y}^{3} - 5 {x}^{2}y - 5x {y}^{2}$