Question

x³y-xy-x³+x
Разложить на множители.

Answer 1

x³y - xy - x³ + x = (x³y - xy) - (x³ - x) = xy(x² - 1) - x(x² - 1) = (x² - 1)(xy - x) = x(y - 1)(x - 1)(x + 1)

Answer 2

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