Question

Разложите на множители: 1. x^2-y^2+x-y 2. 4x^2-4xy+y^2-9 3.ac^4-c^4-ac^2+c^2

Answer 1

$1) x^2-y^2+x-y = (x^2-y^2)+(x-y ) = \\ = (x - y)(x + y) + (x - y) = \\ =(x - y)(x + y + 1) \\ \\ 2) \: 4x^2-4xy+y^2-9 = \\ = 4x(x - y) + (y - 3)(y + 3)\\ \\ 3)ac^4-c^4-ac^2+c^2 = \\ = {c}^{4} (a - 1) - {c}^{2} (a - 1) = \\ = (a - 1)( {c}^{4} - {c}^{2}) = \\ = (a - 1)( {c}^{2} - c)( {c}^{2} + c)$