Verified answer

1) x^2 + y^2 + 2xy - 1 = (x + y)^2 - 1 = (x + y - 1)(x + y + 1)

2) a^2 + b^2 - 2ab - 25 = (a - b)^2 - 25 = (a - b - 5)(a - b + 5)

3) 36 - b^2 - c^2 + 2bc = 36 - (b - c)^2 = (6 - b + c)(6 + b - c)