Question

Разложите на множители 1) а^2-в^2-а+в 3) х^3-х^2у-ху^2+у^3

Answer 1

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