Question

Разложите на множители a²-b²-a+b
a³+a²b-ab²-b³
xc-yc-x²+2xy-y²​

Answer 1

1) a² - b² - a + b = (a² - b²) - (a - b) = (a - b)(a + b) - (a - b) = (a - b)(a + b - 1)

2) a³ + a²b - ab² - b³ = (a³ - b³) + (a²b - ab²) = (a - b)(a² + ab + b²) + ab(a - b) =

= (a - b)(a² + ab + b² + ab) = (a - b)(a² + 2ab + b²) = (a - b)(a + b)(a + b)

3) xc - yc - x² + 2xy  - y² =  (xc - yc) - (x² - 2xy + y²) = c(x - y) - (x - y)² =

= (x - y)(c - x + y)