Разложите многочлен на множители:
а) $(x^2 + 1)^2 - 4x^2$;
б) $(y^2 + 2y)^2 - 1$;
в) $81 - (c^2 + 6c)^2$;
г) $16m^2 - (m - n)^2$.
$(x^2 + 1)^2 - 4x^2 = (x^2 + 1)^2 - (2x)^2 = (x^2 + 1 - 2x)(x^2 + 1 + 2x) = (x^2 - 2x + 1)(x^2 + 2x + 1) = (x - 1)^2(x + 1)^2$
$(y^2 + 2y)^2 - 1 = (y^2 + 2y)^2 - 1^2 = (y^2 + 2y - 1)(y^2 + 2y + 1) = (y^2 + 2y - 1)(y + 1)^2$
$81 - (c^2 + 6c)^2 = 9^2 - (c^2 + 6c)^2 = (9 - (c^2 + 6c))(9 + c^2 + 6c) = (9 - c^2 - 6c)(c^2 + 6c + 9) = (9 - c^2 - 6c)(c + 3)^2$
$16m^2 - (m - n)^2 = (4m)^2 - (m - n)^2 = (4m - (m - n))(4m + (m - n)) = (4m - m + n)(4m + m - n) = (3m + n)(5m - n)$
Пожауйста, оцените решение
