Question

Разложите на множители 3a^3-75ab^2 x-y-x^2+2xy -y^2 (2-x)*(2+x)-a*(a-2x)

Answer 1

$3a^3-75ab^2 = 3a(a^2-25b^2) = 3a(a^2-(5b)^2) = 3a(a-5b)(a+5b) \ ;$

$x-y-x^2+2xy-y^2 = (x-y)-(x^2-2xy+y^2) = \\\\ = (x-y)-(x-y)^2 = (x-y)(1-(x-y)) = (x-y)(1-x+y) \ ;$

$(2-x)(2+x)-a(a-2x) = 2^2-x^2-a(a-2x) = \\\\ = 2^2-x^2-a^2+2ax = 2^2-(x^2-2xa+a^2) = 2^2-(x-a)^2 = \\\\ = (2-(x-a))(2+(x-a)) = (2-x+a)(2+x-a) \ .$