Разложите многочлен на множители:
а) $ax^2 - ay - bx^2 + cy + by - cx^2$;
б) $xy^2 - by^2 - ax + ab + y^2 - a$;
в) $ax + bx + cx + ay + by + cy$;
г) $ab - a^2b^2 + a^3b^3 - c + abc - ca^2b^2$.
$ax^2 - ay - bx^2 + cy + by - cx^2 = (ax^2 - cx^2 - bx^2) - (ay - cy - by) = x^2(a - c - b) - y(a - c - b) = (a - c - b)(x^2 - y)$
$xy^2 - by^2 - ax + ab + y^2 - a = (xy^2 - by^2 + y^2) - (ax - ab + a) = y^2(x - b + 1) - a(x - b + 1) = (x - b + 1)(y^2 - a)$
$ax + bx + cx + ay + by + cy = (ax + bx + cx) + (ay + by + cy) = x(a + b + c) + y(a + b + c) = (a + b + c)(x + y)$
$ab - a^2b^2 + a^3b^3 - c + abc - ca^2b^2 = (ab - a^2b^2 + a^3b^3) - (c - abc + ca^2b^2) = ab(1 - ab + a^2b^2) - c(1 - ab + a^2b^2) = (1 - ab + a^2b^2)(ab - c)$
Пожауйста, оцените решение
