Разложите многочлен на множители:
а) $(y + 2)^2 - 4y^2$;
б) $100a^2 - (5a + 9)^2$;
в) $(t - 7)^2 - 9t^2$;
г) $121b^2 - (7b - 3)^2$.
$(y + 2)^2 - 4y^2 = (y + 2)^2 - (2y)^2 = (y + 2 - 2y)(y + 2 + 2y) = (2 - y)(3y + 2)$
$100a^2 - (5a + 9)^2 = (10a)^2 - (5a + 9)^2 = (10a - (5a + 9))(10a + 5a + 9) = (10a - 5a - 9)(15a + 9) = (5a - 9)(15a + 9) = 3(5a - 9)(5a + 3)$
$(t - 7)^2 - 9t^2 = (t - 7)^2 - (3t)^2 = (t - 7 - 3t)(t - 7 + 3t) = (-2t - 7)(4t - 7) = -(2t + 7)(4t - 7)$
$121b^2 - (7b - 3)^2 = (11b)^2 - (7b - 3)^2 = (11b - (7b - 3))(11b + 7b - 3) = (11b - 7b + 3)(18b - 3) = (4b + 3)(18b - 3) = 3(4b + 3)(6b - 1)$
Пожауйста, оцените решение
